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REVISION TEST - 01 Course : VIJAY (R) TOPIC : KINEMATICS (1-D & RELATIVE MOTION) Time : 3 Hrs.

Max. Marks : 133

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative making). 2. For each correct multiple choice question 4 marks (no negative marking). 3. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 4. For each match the column question 6 marks (no negative marking). 5. For each correct assertion/reason question 3 marks (with 1 mark negative marking).

SINGLE CHOICE QUESTIONS 1.

A particle is projected from origin O with a velocity (30 i + 40 j) m/s. Then the position vector of the particle 5 seconds later is : (take g = 10 m/s2) (A) 150 i + 200j m (B) 150 i + 75 j m (C) 30i + 75j m (D) Nothing can be predicted.

2.

For a particle moving in a straight line, the displacement of the particle at time t is given by S = t3 – 6t2 + 3t + 7 What is the velocity of the particle when its acceleration is zero? (A) – 9 m s–1 (B) – 12 m s–1 (C) 3 m s–1 (D) 42 m s–1

3.

The velocity of a particle moving on the x-axis is given by v = x2 + x where v is in m/s and x is in m. Find its acceleration in m/s2 when passing through the point x = 2m (A) 0 (B) 5 (C) 11 (D) 30

4.

A parachutist drops freely from an aeroplane for 10 s before the parachute opens out. Then he descends with a net retardation of 2.5 ms–2. If he bails out of the plane at a height of 2495 m and g = 10 ms–2, his velocity on reaching the ground will be (A) 2.5 ms–1 (B) 7.5 ms–1 (C) 5 ms–1 (D) 10 ms–1

5.

A particle can travel from point A to B from two different paths 1 and 2, as shown, in same interval of time. Then which of the following is incorrect? (A) Average velocity along the two paths must be equal (B) The particle may travel along both the paths unaccelerated (C) The direction of instantaneous velocity along the path 1 & 2 can be same for a maximum of two point on the paths. (D) The average and instantaneous velocity along path 1 can have same direction.

6.

Two trains, which are moving along different tracks in opposite directions, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are 300 m apart. Graphs given below show their velocities as function of time as the trains slow down. The separation between the trains when both have stopped, is :

(A) 120 m

RESONANCE

(B) 280 m

(C) 60 m

(D) 20 m.

1

7.

Position (Km) - Time (min.) graph is shown for two cars ‘A’ and ‘B’. Both collide at time t = 150 minute. Then the distance of position ‘R’ of accident from the starting point ‘Q’ of car A will be. (Initial distance between the two cars is 500 km) (Position in the graph shows the distance of the two cars from the point ‘Q’) (A) 200 km (B) 300 km (C) 250 km (D) 400 km

8.

A particle starts from rest with uniform acceleration and its velocity after n seconds is v. The displacement of the body in last two seconds is (A)

v(n 1) n

(B)

2v(n 1) n

(C)

2v(n 1) n

(D)

v(n 1) n

9.

A boat is rowed across a river at the rate of 4.5 km/hr. The river flows at the rate of 6 km/hr. The velocity of boat in m/s is: (A) 3.1 (B) 2.1 (C) 2.9 (D) 5

10.

An aeroplane is to go along straight line from A to B, and back again. The relative speed with respect to wind is V.. The wind blows perpendicular to line AB with speed . The distance between A and B is l. The total time for the round trip is: 2

(A) 11.

2

V v

2

(B)

2v 2

V v

2

(C)

2

2V 2

V v

2

A man can swim in still water with a speed of 3 m/s. x and y axis are drawn along and normal to the bank of river flowing to right with a speed of 1 m/s. The man starts swimming from origin O at t = 0 second. Assume size of man to be negligible. Find the equation of locus of all the possible points where man can reach at t = 1 sec. (A) (x – 1)2 + y2 = 3 (B) (x – 1)2 + y2 = 9 2 2 (C) x + (y – 1) = 3 (D) x2 + (y – 1)2 = 9

(D)

V 2 v 2 y Vriver=1m/s

river

flow x

O

12.

P is a point moving with constant speed 10 m/s such that its velocity vector always maintains an angle 60° with line OP as shown in figure (O is a fixed point in space). The initial distance between O and P is 100 m. After what time shall P reach O. (A) 10 sec. (B) 15 sec. (C) 20 sec. (D) 20 3 sec

13.

During a rainy day, rain is falling vertically with a velocity 2m/s. A boy at rest starts his motion with a constant acceleration of 2m/s2 along a straight road. Find the rate at which the angle of the axis of umbrella with vertical should be changed so that the rain always falls parallel to the axis of the umbrella. (A)

1 1 t

2

(B)

2 1 t

2

(C)

1 2t

2

(D)

1 1 2t 2

14.

A train is standing on a platform , a man inside a compartment of a train drops a stone . At the same instant train starts to move with constant acceleration . The path of the particle as seen by the person who drops the stone is : (A) parabola (B) straight line for sometime & parabola for the remaining time (C) straight line (D) variable path that cannot be defined

15.

Two boats A and B having same speed relative to river are moving in a river. Boat A moves normal to the river current as observed by an observer moving with velocity of river current. Boat B moves normal to the river as observed by the observer on the ground. (A) To a ground observer boat B moves faster than A (B) To a ground observer boat A moves faster than B (C) To the given moving observer boat B moves faster than A (D) To the given moving observer boat A moves faster than B

RESONANCE

2

16.

For four particles A, B, C & D, the velocities of one with respect to other are given as V DC is 20 m/s towards north, V BC is 20 m/s towards east and V BA is 20 m/s towards south. Then V DA is (A) 20 m/s towards north (B) 20 m/s towards south (C) 20 m/s towards east (D) 20 m/s towards west

MULTIPLE CHOICE QUESTIONS 17.

A particle moves in xy plane in such a way that its distance ‘r’ from the origin depends upon time ‘t’ as r = 3t. The angle ‘’ made by its position vector with the positive x-axis at any time ‘t’ is given as ; = 2t. Here r is in metres, in rad and t in seconds. (A) The particle moves in circular motion. (B) At time t = 0.5 s, its speed is 3 2 m/s. (C) At time t = 0.5 s, its velocity vector makes an angle 45° with its position vector at the same time. (D) At time t = 0.5 s, its velocity vector makes an angle 30° with its position vector at the same time.

18.

Two particles, one with constant velocity 50m/s and the other with uniform acceleration 10m/s 2, start moving simultaneously from the same position in the same direction. They will be at a distance of 125m from each other after (A) 5 sec. (B) 5(1 + 2) sec. (C) 10sec. (D) 10(2 + 1)sec.

19.

A man standing on the edge of the terrace of a high rise building throws a stone vertically up with a speed of 20 m/s. Two seconds later an identical stone is thrown vertically downwards with the same speed of 20 m/s. Then: (A) the relative velocity between the two stones remain constant till one hits the ground (B) both will have the same kinetic energy when they hit the ground (C) the time interval between their hitting the ground is 2 seconds (D) if the collisions on the ground are perfectly elastic both will rise to the same height above the ground.

20.

A cart with a mass M = 1/2 kg is connected by a string to a weight of mass m = 200 g. At the initial moment the cart moves to the left along a horizontal plane at a speed V0 = 7 ms 1. All the surfaces are smooth (g = 9.8 ms 2) (A) the distance covered by cart in 5 s is zero (B) after 5 s weight of mass m will be in same position (C) the distance covered by cart in 5 s is 17.5 m (D) none of the above A particle moves with an initial velocity v 0 and retardation v, where v is its velocity at any time t ( is a positive constant). (A) the particle will cover a total distance of v 0/ (B) the particle will continue to move for a very long time (C) the particle will stop shortly (D) the velocity of particle will become v 0/2 after time 1/.

21.

22.

A particle is moving rectilinearly so that its acceleration is given as a = 3t2+1 m/s2.Its initial velocity is zero. (A) The velocity of the particle at t=1 sec will be 2m/s. (B) The displacement of the particle in 1 sec will be 2m. (C) The particle will continue to move in positive direction. (D) The particle will come back to its starting point after some time.

23.

A man is standing on a road and observes that rain is falling at angle 45º with the vertical. The man starts running on the road with constant acceleration 0.5 m/s 2. After a certain time from the start of the motion, it appears to him that rain is still falling at angle 45º with the vertical, with speed 2 2 m/s . Motion of the man is in the same vertical plane in which the rain is falling. Then which of the following statement(s) are true. (A) It is not possible (B) Speed of the rain relative to the ground is 2 m/s. (C) Speed of the man when he finds rain to be falling at angle 45º with the vertical, is 4m/s. (D) The man has travelled a distance 16m on the road by the time he again finds rain to be falling at angle 45°.

RESONANCE

3

COMPREHENSION Comprehension - 1 Raindrops are falling with a velocity 10 2 m/s making an angle of 450 with the vertical. The drops appear to be falling vertically to a man running with constant velocity. The velocity of rain drops change such that the rain drops now appear to be falling vertically with 3 times the velocity it appeared earlier to the same person running with same velocity. 24.

The magnitude of velocity of man with respect to ground is (A) 10 2 m/s

25.

(C) 20 m/s

(D) 10 m/s

After the velocity of rain drops change, the magnitude of velocity of raindrops with respect to ground is (A) 20 m/s

26.

(B) 10 3 m/s

(B) 20 3 m/s

(C) 10 m/s

(D) 10 3 m/s

The angle (in degrees) between the initial and the final velocity vectors of the raindrops with respect to the ground is (A) 8 (B) 15 (C) 22.5 (D) 37

Comprehension - 2 A overhead bridge, a subway and a road start from A and again meet at B. The minimum distance between A and B, which is same as the length of the road AB, is 2 km. The overbridge and the subway form a semicircular arc above and below the road. A laser sensor is fixed (embedded) in the road. An Autorickshaw takes the overbridge from A and a taxi takes the subways from B.The laser sensor gives a beep when the linear distances between point A and the autorickshaw is same as that between the rickshaw and the laser sensor which also equals the distance of laser source from point A. 27.

If the time t, for the laser starts when the autorickshaw just enters the bridge from point A and at t = 240 sec, laser the gives a beep, what is the speed of the autorickshaw ? (A) 4.36 m/s (B) 1.21 m/s (C) 8.16 m/s (D) 16.32 m/s

28.

The autorickshaw takes the overhead bridge from A and on reaching B, immediately takes the subway to come back to A, while the taxi starts from B travels to and fro from B to A continuously by road. If the auto and the taxi travel with constant speeds of

km/hr and 3 km/hr respectively, how frequently do 2

they meet at A ? (A) every 4 hours

(C) every 29.

(B) every

2 hours 3

2n hours, n = 3,6,9,.... 3

(D) they never meet

Due to heavy rains, the flyover and the roads were blocked and all the vehicles had to take the subway. The autorickshaw and the taxi started from A and B respectively with the speeds

2 and km/hr 3 2

respectively. After how much time did they meet ? (A)

7 hours 6

RESONANCE

(B)

6 hours 7

(C)

2 hours 3

(D)

6 hours 7

4

Comprehension - 3 Mr. Shyam drives his car at uniform speed from bottom of a mountain to the top in 20 minutes along a helical path as shown. At the beginning the speedometer of his car shows 8315 km, while on reaching the top it reads 8335 km.(Take upward as positive yaxis and positive x-axis towards right) 30.

31.

The total distance covered is : (A) 10 km (B) 20 km

(D) can not be determine

His displacement vector during the journey is : (A) ( 3 ˆi 4 ˆj ) km

32.

(C) 25 km

(B) 3 km

(C) 5 km

(D) none of these

(C) (25/8) m/s

(D) None of these

The average velocity during the journey is : (A) (9 ˆi 12ˆj) km/hr

(B) (2.5 ˆi 3.3 ˆj) m/s

MATCH THE COLUMN 33.

Two particles A and B moving in x-y plane are at origin at t = 0 sec. The initial velocity vectors of A and B are u A = 8 ˆi m/s and uB = 8 ˆj m/s. The acceleration of A and B are constant and are a A = –2 ˆi m/s 2 and a B = – 2 ˆj m/s 2. Column gives certain statements regarding particle A and B. Column gives corresponding results. Match the statements in column with corresponding results in Column . Column I Column II

34.

(A) The time (in seconds) at which velocity of A relative to B is zero

(p) 16 2

(B) The distance (in metres) between A and B when their relative velocity is zero. (C) The time (in seconds) after t = 0 sec, at which A and B are at same position (D) The magnitude of relative velocity of A and B at the instant they are at same position.

(q) 8 2 (r) 8 (s) 4

A particle is moving along a straight line. Its velocity varies with time as v = kt, where k is a positive constant and t is the time. Match the graphs in Column with the statements in Column Column Column

(A) Acceleration versus time curve

(p)

(B) Acceleration versus displacement curve

(q)

(C) Velocity versus time curve

(r)

(D) Displacement versus velocity curve

(s)

RESONANCE

5

ASSERTION / REASON 35.

Assertion : If acceleration of a particle is decreasing then it is possible that velocity is increasing with time. Reason : Acceleration is rate of change of velocity. (A) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. (B) If both Assertion and Reason are true, but Reason is not correct explanation of the Assertion. (C) if Assertion is true, but the Reason is false. (D) if Assertion is false, but the Reason is true.

36

STATEMENT–1 : The equation of distance travelled by a particle moving in a straight line with constant acceleration in nth second is Sn = u + (2n – 1)

a , where letters have usual meaning, is dimensionally 2

incorrect. STATEMENT–2: For every equation relating physical quantities to be true, it must have dimensional homogenity. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. 37.

STATEMENT-1 : The magnitude of velocity of two boats relative to river is same. Both boats start simultaneously from same point on one bank may reach opposite bank simultaneously moving along different paths. STATEMENT-2 : For boats to cross the river in same time. The component of their velocity relative to river in direction normal to flow should be same. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

Answer Key (Revision Test - 01) 1. 6. 11. 16. 21. 26. 31. 34.

(B) 2. (D) 7. (B) 12. (D) 17. (A)(B) 22. (B) 27. (A) 32. (A) p (B) p (C) q (D) r

(A) (B) (C) (B)(C) (A)(C) (A) (A)

3. 8. 13. 18. 23. 28. 33. 35.

(D) 4. (C) (C) 9. (B) (A) 14. (C) (A)(B) 19. (A)(B)(C)(D) (C)(D) 24. (D) (D) 29. (B) (A) s (B) p (C) r (D) q (A) 36 (D)

5. 10. 15. 20. 25. 30.

(B) (A) (B) (B) (C) (A) (B)

37.

(A)

Solution will be provided with next revision test.

RESONANCE

6

REVISION TEST - 02 COURSE : VIJAY (R) TOPIC : PROJECTILE MOTION SUBJECT : PHYSICS Time : 1½ Hrs.

Max. Marks : 48

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative making). 2. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 3. For each match the column question 6 marks (no negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking).

SINGLE CHOICE QUESTIONS 1.

A particle when projected in vertical plane moves along the fixed smooth surface with initial velocity 20 m/s at an angle of 60º, so that its normal reaction on the surface remains zero throughout the motion. Then the slope of the tangent to the surface at height 5 m from the point of projection A will be: (A) 30º

2.

(B) 45º

(D) tan1 2

A particle moves along the parabolic path y = ax2 in such a way that the y-component of the velocity remains constant, say c. The x and y coordinates are in meters. Then acceleration of the particle at x =1 m is (A) ac kˆ

3.

(C) tan1 2

(B) 2ac 2 ˆj

(C)

c2 ˆ i 4a 2

(D)

c ˆ i 2a

An object is thrown from a point ‘A’ horizontally from a tower and hits the ground 3s later at B. The line from ‘A’ to ‘B’ makes an angle of 30º with the horizontal. The initial velocity of the object is : (take g = 10 m/s2) (A) 15 3 m/s

(B) 15 m/s

(C) 10

(D) 25 / 3 m/s

3 m/s

4.

A particle is projected from a point P (2, 0, 0)m with a velocity 10 m/s making an angle 45º with the horizontal. The plane of projectile motion passes through a horizontal line PQ which makes an angle of 37º with positive x-axis, xy plane is horizontal. The coordinates of the point where the particle will strike the line PQ is: (Take g = 10 m/s 2) (A) (10, 6, 0)m (B) (8, 6, 0)m (C) (10, 8, 0)m (D) (6, 10, 0)m

5.

A car starts with constant acceleration a = 2m/s2 at t = 0. Two coins are released from the car at t = 3 & t = 4. Each coin takes 1 second to fall on ground. Then the distance between the two coins will be (Assume coin sticks to the ground) (A) 9 m (B) 7 m (C) 15 m (D) 2m

6.

Velocity of a stone projected, 2 second before it reaches the maximum height, makes angle 53° with the horizontal then the velocity at highest point will be (A) 20 m/s (B) 15 m/s (C) 25 m/s (D) 80/3 m/s Two guns are mounted (fixed) on two vertical cliffs that are very high from the ground as shown in figure. The muzzle velocity of the shell from G1 is u1 and that from G2 is u2. The guns aim exactly towards each other The ratio u1 : u2 such that the shells collide with each other in air is (Assume that there is no resistance of air)

7.

(A) 1 : 2 (C) will not collide for any ratio 8.

(B) 1 : 4 (D) will collide for any ratio

A stone is projected from level ground such that its horizontal and vertical components of initial velocity are ux = 10 m/s and uy = 20 m/s respectively. Then the angle between velocity vector of stone one second before and one second after it attains maximum height is : (A) 30° (B) 45° (C) 60° (D) 90°

COMPREHENSION Comprehension A stone is projected from level ground with speed u and at an angle with horizontal. Some how the acceleration due to gravity (g) becomes double (that is 2g) immediately after the stone reaches the maximum height and remains same thereafter. Assume direction of acceleration due to gravity always vertically downwards.

RESONANCE

1

9.

The total time of flight of particle is :

3 u sin (A) 2 g 10.

(B)

u sin g

1 1 2

(C)

2u sin g

(D)

u sin 1 2 g 2

The horizontal range of particle is

u 2 sin 2 1 u 2 sin 2 1 3 u2 sin 2 u2 1 (C) 2 (B) sin2 (D) 2g 2g 4 g g 2 2 The angle which the velocity vector of stone makes with horizontal just before hitting the ground is given by : (A) tan = 2 tan (B) tan = 2 cot (C) tan = 2 tan (D) tan = 2 cot (A)

11.

MATCH THE COLUMN 12.

Match the following. The projectile collides perpendicularly with the inclined plane. (Refer the figure) u

(a) Maximum height attained by the projectile from the ground

(P) zero

(b) Maximum height attained by the projectile from Inclined plane

(Q) g

(c) Acceleration of the projectile before

(R)

u 2 sin 2 2 g cos

(S)

u 2 sin 2 ( ) 2g

striking the inclined plane (d) Horizontal component of acceleration of the projectile.

13.

Assertion : For a projectile up the incline maximum angle of projection can be where is angle 4 2 made by incline with horizontal.

Reason : Maximum range up the incline is given by

u2 where is angle made by incline with g(1 sin )

horizontal.. (A) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. (B) If both Assertion and Reason are true, but Reason is not correct explanation of the Assertion. (C) if Assertion is true, but the Reason is false. (D) if Assertion is false, but the Reason is true. 14.

STATEMENT-1 : Two stones are simultaneously projected from level ground from same point with same speeds but different angles with horizontal. Both stones move in same vertical plane. Then the two stones may collide in mid air. STATEMENT-2 : For two stones projected simultaneously from same point with same speed at different angles with horizontal, their trajectories may intersect at some point. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

Answer Key (Revision Test - 02) 1. 8. 13.

(D) (D) (D)

2. 9. 14.

(C) (B) (D)

3. 10.

(A) (B)

4. 11.

(A) (C)

5. 12.

(A) (a) S

6. (B) 7. (b) R (c) Q (d) P

(D)

Solution will be provided with next revision test.

RESONANCE

2

REVISION TEST - 03 COURSE : VIJAY (R) TOPIC : NLM & Friction SUBJECT : PHYSICS Time : 3 Hrs.

Max. Marks : 104

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative making). 2. For each correct multiple choice question 3 marks (with 1 mark negative making). 3. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking). 5. For each correct subjective question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

Two blocks A & B with mass 4 kg and 6 kg respectively are connected by a stretched spring of negligible mass as in figure. When the two blocks are released simultaneously the initial acceleration of B is 1.5 m/s 2 westward. The acceleration of A is : (A) 1 m/s 2 westward (B) 2.25 m/s 2 eastward (C) 1 m/s 2 eastward (D) 2.75 m/s 2 westward

2.

System shown in figure is in equilibrium. The magnitude of change in tension in the string just before and just after, when one of the spring is cut. Mass of both the blocks is same and equal to m and spring constant of both springs is k. (Neglect any effect of rotation) (A)

3.

4.

mg 2

(B)

mg 4

(C)

3m g 4

(D)

3m g 2

In the figure a block ‘A’ of mass ‘m’ is attached at one end of a light spring and the other end of the spring is connected to another block ‘B’ of mass 2m through a light string. ‘A’ is held and B is in static equilibrium. Now A is released. The acceleration of A just after that instant is ‘a’. In the next case, B is held and A is in static equilibrium. Now when B is released, its acceleration immediately after the release is 'b'. The value of a/b is : (Pulley, string and the spring are massless) 1 (A) 0 (B) undefined (C) 2 (D) 2 In the figure, at the free end of the light string, a force F is applied to keep the suspended mass of 18 kg at rest. Then the force exerted by the ceiling on the system (assume that the string segments are vertical and the pulleys are light and smooth) is: (g= 10 m/s2) (A) 60 N (D) 240 N

(B) 120 N (E) 200 N

(C) 180 N

5.

Two massless rings slide on a smooth circular loop of the wire whose axis lies in a horizontal plane. A smooth massless inextensible string passes through the rings, which carries masses m1 & m2 at the two ends and mass m3 between the rings. If there is equilibrium when the line connnecting each ring with centre substends an angle 300 with vertical as shown in figure. Then the ratio of masses are (A) m1 = 2m2 = m3 (B) 2m1 = m2 = 2m3 (C) m1 = m2 = m3 (D) None of these

6.

Four identical metal butterflies are hanging from a light string of length 5 at equally 1 placed points as shown. The ends of the string are attached to a horizontal fixed support. The middle section of the string is horizontal. The relation between the 2 angle 1 and 2 is given by (A) sin1 = 2 sin2 (B) 2cos1 = sin2 (C) tan1 = 2 tan2 (D) 2 < 1 and no other conclusion can be derived.

RESONANCE

1

7.

A bob is hanging over a pulley inside a car through a string . The second end of the string is in the hand of a person standing in the car . The car is moving with constant acceleration 'a' directed horizontally as shown in figure . Other end of the string is pulled with constant acceleration ' a ' (relative to car) vertically. The tension in the string is equal to (A) m g2 a 2

8.

(B) m g2 a 2 – ma

(D) m(g + a)

A wedge of height 'h' is released from rest with a light particle P placed on it as shown. The wedge slides down an incline which makes an angle with the horizontal. All the surfaces are smooth, P will reach the surface of the incline in time 2h

(A)

9.

(C) m g2 a 2 + ma

2

gsin

(B)

2h g sin cos

(C)

2h g tan

2h

(D)

g cos 2

In the given arrangement, mass of the block is M and the surface on which the block is placed is smooth. Assuming all pulleys to be massless and frictionless, strings to be inelastic and light, R1, R2 and R3 to be light supporting rods, then acceleration of point ‘P’ will be (Ais fixed) : (A) 0

(B)

(C)

4F m

(D)

2F m

10.

In the arrangement shown in the figure mass of the block B and A are 2 m,, 8 m respectively. Surface between B and floor is smooth. The block B is connected to block C by means of a pulley. If the whole system is released then the minimum value of mass of the block C so that the block A remains stationary with respect to B is : (Co-efficient of friction between A and B is and pulley is ideal) 10m m 2m 10 m (A) (B) (C) (D) 1 1 1

11.

A plank is held at an angle to the horizontal (Fig.) on two fixed supports A and B. The plank can slide against the supports (without friction) because of its weight Mg. With what acceleration and in what direction, a man of mass m should move so that the plank does not move. m (A) g sin 1 down the incline M

M (B) g sin 1 down the incline m

m (C) g sin 1 up the incline M

M (D) g sin 1 up the incline m

12.

A block of mass 20 kg is acted upon by a force F = 30 N at an angle 53° with the F horizontal in downward direction as shown. The coefficient of friction between the 53° block and the horizontal surface is 0.2. The friction force acting on the block by the ground is (g = 10 m/s2) (A) 40.0 N (B) 30.0 N (C) 18.0 N (D) 44.8 N

13.

A particle is resting over a smooth horizontal floor. At t = 0, a horizontal force starts acting on it. Magnitude of the force increases with time according to law F = t, where is a positive constant and t is time. For the figure shown which of the following statements is/are correct? (A) Curve 1 shows acceleration against time (C) Curve 2 shows velocity against acceleration

RESONANCE

(B) Curve 2 shows velocity against time (D) none of these 2

14.

An insect of mass m, starts moving on a rough inclined surface from point A. As the surface is very sticky, the coefficient of friction between the insect and the incline is = 1. Assume that it can move in any

A =1

direction ; up the incline or down the incline then (A) The maximum possible acceleration of the insect can be 14 m/sec 2 (B) The maximum possible acceleration of the insect can be 2 m/sec 2 (C) The insect can move with a constant velocity

=37°

(D) The insect can not move with a constant velocity Comprehension A block of mass M is kept in elevator (lift) which starts moving upward with constant acceleration 'b' as shown in figure. Initially elevator at rest. The block is observed by two observers A and B for a time interval t = 0 to t = T. Observer B is at rest with respect to elevator and observer A is standing on the ground.

15.

The observer A finds that the work done by gravity on the block is -

1 1 1 1 Mg2T2 (B) – Mg2T2 (C) Mg bT2 (D) – Mg bT2 2 2 2 2 The observer A finds that work done by normal reaction acting on the block is (A)

16.

(A)

1 M(g + b)2T2 2

(B) –

1 M(g + b)2T2 2

(C)

1 M(g + b) bT2 2

(D) –

1 M(g + b) bT2 2

17.

According to observer B (A) The work done by gravity on the block is zero (B) The work done by normal reaction on the block is zero (C) The work done by pseudo force on the block is zero (D) All the above are correct Q.18 to 23 (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 and Statement-2 both are False. (E) Statement-1 is False, Statement-2 is True. 18. Assertion (A) : If a body is not in rest position then the net external force acting on it cannot be zero. Reason (R) : If a body is moving with uniform speed it will continue doing so unless frictional force exceeds the force of motion. 19.

Assertion (A) : Two bodies of mass 50g and 20g are allowed to fall from the same height. If air resistance for each is same, then both the bodies reach the earth simultaneously. Reason (R) : Acceleration of both the bodies is same.

20.

Assertion (A) : Air is thrown on a sail attached to a boat from an electric fan placed on the boat, because of which some movement is caused in the boat. Reason (R) : When the fan pushes the sail by the air, then air also pushes the fan in the opposite direction, causing motion.

21.

Assertion (A) : A bird sitting on the floor of a wire cage and cage is in the hand of a boy. Even when the bird starts flying in the cage, the boy does not experience any change in the weight of the cage. Reason (R) : Bird is still in the cage because of which the boy does not experience any change.

RESONANCE

3

22.

Assertion (A) : A soda water bottle is falling freely the bubbles of the gas will not rise in water. Reason (R) : Pressure in the water does not increase with depth.

23.

Assertion (A) : When a ball is thrown upwards, its momentum first decreases and then increases. Reason (R) : Law of conservation of momentum is not followed is this process.

24.

Figure shows a moving truck, in which there is a bob 'A' and a block 'B' attached to a spring kept on the rough floor of truck. With respect to truck, (g = 10 m/sec 2) (Assume spring is massless) (a)

If bob A is in equilibrium at = 30º, the spring is in its natural state and the block B (mass =

3 kg) is also in equilibrium , find the minimum value of the coefficient of static friction between the block and the floor of truck. If now the acceleration of truck is changed so that the new angular position of A for which it is again in equilibrium is 45º, find the minimum elongation in spring when block B is in equilibrium assuming the value of the coefficient of static friction as that calculated in part (a).

(b)

25.

Collar A starts from rest & moves to the left with a constant acceleration. Knowing that after 30 s, the relative velocity of collar B w.r.t. collar A is 900 mm/s, determine the accelerations of A and B.

26.

In the arrangement shown in Figure mass of blocks A, B and C is 18.5 kg, 8 kg and 1.5 kg respectively. All the surfaces are smooth. System is released from rest at t = 0 & pulleys are light & frictionless. Calculate acceleration of block C.

27.

Figure shows an ideal pulley block of mass m = 1 kg, resting on a rough ground with friction coefficient µ = 1.5. Another block of mass M = 11 kg is hanging as shown. When system is released it is found that the magnitude of acceleration of point P on string is a. Find value of 4a in m/s2. (Use g = 10 m/s2)

28.

In which of the following cases the magnitude of acceleration of the block A will be maximum (Neglection friction, mass of pulley and string)

(i)

(ii)

m A

(iii)

m A

2m

m smooth

m

A

A

(iv)

2mg 2mg

B 2m

Answer Key (Revision Test - 03) 1. 7. 13. 19.

B C A,B,C D

2. 8. 14. 20.

24.

(a)

26. 27.

(i) 10 ms2 13

28.

(i) a =

A A A,C D

1 (b)

3

3. 9. 15. 21.

C C D D

3 1

4. 10. 16. 22.

D D C A

5. 11. 17. 23.

25.

10mm/s2

C B D A

6. 12. 18.

C C D

(ii) 0. 19 joule

2mg mg g = 3m 3

(ii) a =

2mg mg =g m

(iii) a =

2mg = 2g m

(iv) a =

2g 3

Solution will be provided with next revision test.

RESONANCE

4

REVISION TEST - 04 SUBJECT : PHYSICS Course : VIJAY (R) TOPIC : WPE & Circular Motion Time : 3 Hrs.

Max. Marks : 158

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative marking). 2. For each correct multiple choice question 4 marks (with 1 mark negative marking). 3. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 4. For each correct answer in match the column 6 marks (with no negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking). 5. For each correct subjective question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

2.

Select the correct alternative. (A) Work done by kinetic friction on a body always results in a loss of its kinetic energy. (B) Work done on a body, in the motion of that body over a close loop is zero for every force in nature. (C) Total mechanical energy of a system is always conserved no matter what type of internal and external forces on the body are present. (D) When total work done by a conservative force on the system is positive then the potential energy associated with this force decreases. A body of mass 1 kg is shifted from A to D on inclined planes by applying a force slowly such that the block is always is in contact with the plane surfaces. Neglecting the jerk experienced at points C and B, total work done by the force is :

(A) 90 J

(B) 56 J

(C) 180 J

(D) 0 J

3.

The cart starting from rest moves down the incline. When the cart maximally compresses the spring (that is compression in the spring is maximum) at the bottom of the track, the cart’s (A) velocity and acceleration are zero. (B) velocity is nonzero but its acceleration is zero. (C) acceleration is nonzero, but its velocity is zero. (D) velocity and acceleration are both nonzero.

4.

A horse drinks water from a cubical container of side 1 m. The level of the stomach of horse is at 2 m from the ground. Assume that all the water drunk by the horse is at a level of 2 m from the ground. Then minimum work done by the horse in drinking the entire water of the container is (Take water = 1000 kg/m3 and g = 10 m/s2 ) : (A) 10 kJ

RESONANCE

(B) 15 kJ

(C) 20 kJ

(D) zero

1

5.

A man places a chain (of mass ‘m’ and length ‘ ’) on a table slowly. Initially the lower end of the chain just touches the table. The man drops the chain when half of the chain is in vertical position. Then work done by the man in this process is : (A) – mg

2

(B) –

mg 4

(C) –

3mg 8

(D) –

mg 8

6.

In the track shown in figure section AB is a quadrant of a circle of 1 metre radius. A block is released at A and slides without friction until it reaches B. After B it moves on a rough horizontal floor and comes to rest at distance 3 metres from B. What is the coefficient of friction between floor and body ? (A) 1/3 (B) 2/3 (C) 1/4 (D) 3/8

7.

A particle of mass m moving along a straight line experiences force F which varies with the distance travelled as shown in the figure. If the velocity of the particle at x 0 is

(A) 2

2 F0 x 0 m

2 F0 x 0 , then velocity at 4 x 0 is: m

(B) 2

F0 x 0 m

(C)

F0 x 0 m

(D) none of these

8.

A block of mass m starts at rest at height h on a frictionless inclined plane. The block slides down the plane, travels across a rough horizontal surface with coefficient of kinetic friction , and compresses a spring with force constant k a distance x before momentarily coming to rest. Then the spring extends and the block travels back across the rough surface, sliding up the plane. The block travels a total distance d on rough horizontal surface. The correct expression for the maximum height h’ that the block reaches on its return is: (A) mgh’ = mgh – mgd (B) mgh’ = mgh + mgd (C) mgh’ = mgh + mgd + kx2 (D) mgh’ = mgh – mgd – kx2

9.

The figure shows a hollow cube of side 'a' of volume V. There is a small chamber of volume

V in the cube as 4 shown. This chamber is completely filled by m kg of water. Water leaks through a hole H and spreads in the whole cube. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is :

3 5 1 1 mg a (B) mg a (C) mga (D) mga 8 8 8 2 A particle is moving in a circular path. The acceleration and momentum vectors at an instant of time are ˆ a = 2 ˆi + 3 j m/s2 and P = 6 ˆi – 4 ˆj kgm/s. Then the motion of the particle is

(A) 10.

(A) uniform circular motion (C) circular motion with tangential retardation

RESONANCE

(B) circular motion with tangential acceleration (D) we cannot say anything from a and P given here.

2

11.

A bead of mass m is located on a parabolic wire with its axis vertical and vertex at the origin as shown in figure and whose equation is x2 = 4ay. The wire frame is fixed and the bead can slide on it without friction. The bead is released from the point y = 4a on the wire frame from rest. The tangential acceleration of the bead when it reaches the position given by y = a is :

(A) 12.

g 2

(B)

g

3g 2

(C)

g (D)

2

5

TTwo particles tied to different strings are whirled in a horizontal circle as shown in figure. The ratio of lengths of the strings so that they complete their circular path with equal time period is:

(A)

3 2

(B)

2 3

(C) 1

(D) None of these

13.

A smooth and vertical cone-shaped funnel is rotated with an angular velocity in such a way that an object on the inner wall of the funnel is at rest w.r.t. the funnel. If the object is slightly displaced along the slope from this position and released : (A) it will be in equilibrium at its new position. (B) it will execute SHM (C) it will oscillate but the motion is not SHM (D) none of these

14.

A ring of radius R lies in vertical plane. A bead of mass ‘m’ can move along the ring without friction. Initially the bead is at rest at the bottom most point on ring. The minimum constant horizontal speed v with which the ring must be pulled such that the bead completes the vertical circle (A)

15.

3gR

(C)

4gR

(D)

5gR

5 . 5 gR

A simple pendulum is oscillating in a vertical plane. If resultant acceleration of bob of mass m at a point A is in horizontal direction, find the tangential force at this point in terms of tension T and mg. (A) mg

16.

(B)

(B)

mg T

T 2 (mg)2

(C)

mg T

(mg)2 T 2

T (D) mg

(mg)2 T 2

The member OA rotates about a horizontal axis through O with a constant counter clockwise velocity = 3 rad/sec. As it passes the position = 0, a small mass m is placed upon it at a radial distance r = 0.5 m. If the mass is observed to slip at = 37º, the coefficient of friction between the mass & the member is ______.

(A)

3 16

RESONANCE

(B)

9 16

(C)

4 9

(D)

5 9

3

17.

A bob is attached to one end of a string other end of which is fixed at peg A. The bob is taken to a position where string makes an angle of 300 with the horizontal. On the circular path of the bob in vertical plane there is a peg ‘B’ at a symmetrical position with respect to the position of release as shown in the figure. If Vc and Va be the minimum speeds in clockwise and anticlockwise directions respectively, given to the bob in order to hit the peg ‘B’ then ratio Vc : Va is equal to : (A) 1 : 1

18.

(B) 1 :

(D) 1 : 4

A disc of radius R has a light pole fixed perpendicular to the disc at the circumference which in turn has a pendulum of length R attached to its other end as shown in figure. The disc is rotated with a constant angular velocity . The string is making an angle 300 with the rod. Then the angular velocity of disc is: 1/ 2

3 g (A) R 19.

(C) 1 : 2

2

1/ 2

g (C) 3R

3 g (B) 2R

1/ 2

2g (D) 3 3R

1/ 2

An automobile enters a turn of radius R. If the road is banked at an angle of 450 and the coefficient of friction is 1, the minimum and maximum speed with which the automobile can negotiate the turn without skidding is :

rg rg rg and rg (B) and rg (C) and 2 rg (D) 0 and infinite 2 2 2 A particle is projected horizontally from the top of a tower with a velocity v0. If v be its velocity at any instant, then the radius of curvature of the path of the particle at the point (where the particle is at that instant) is directly proportional to : (A) v3 (B) v2 (C) v (D) 1/v (A)

20.

MULTIPLE CHOICE QUESTIONS 21.

A double conical pendulum consists of two masses, m and M, connected by a massless string passing over a frictionless, massless pulley. The entire apparatus rotates freely at constant angular speed (rad/s) about the vertical axis (dashed line) passing through centre of pulley as shown. After the system comes in steady state, the length of string on either sides of pulley are small and L. Pick up the correct option(s).

(A)

cos m cos M

(B) cos =

g 2L

(C) m = ML

(D) cos =

g 2

22.

One of the forces acting on a particle is conservative then which of the following statement(s) are true about this conservative force (A) Its work is zero when the particle moves exactly once around any closed path. (B) Its work equals the change in the kinetic energy of the particle (C) Then that particular force must be constant. (D) Its work depends on the end points of the motion, not on the path between.

23.

In the figure, a block rests on the top of a smooth fixed hemispherical tube of radius R in which it can just fit. Two springs are connected to the base as shown. The block is given a small jerk so that it can slide on the hemisphere. The F-X (F is magnitude of force and x is compression) graph for the springs is given below. Which of the following may be possible : (A) The block will compress both springs by same amount. (B) The block will compress the springs during its to and fro motion about its original position by different amounts. (C) The block will perform to and fro motion along the hemispherical surface about the original position. (D) The block can never come to the original position.

RESONANCE

4

Comprehension One end of massless inextensible string of length is fixed and other end is tied to a small ball of mass m. The ball is performing a circular motion in vertical plane. At the lowest position, speed of ball is

24.

25. 26.

20 g .

Neglect any other forces on the ball except tension force and gravitational force. Acceleration due to gravity is g. Motion of ball is in nature of (A) circular motion with constant speed (B) circular motion with variable speed (C) circular motion with constant angular acceleration about centre of the circle. (D) none of these At the highest position of ball, tangential acceleration of ball is (A) 0 (B) g (C) 5 g (D) 16 g During circular motion, minimum value of tension in the string (A) zero (B) mg (C) 10 mg

(D) 15 mg

Comprehension : A body of mass m is moving along x-axis under the influence of conservative force with a potential energy given by

U(x) =

cx 2

x a2 Where c and a are positive constants. When displaced slightly from stable equilibrium position x = x0, it will experience restoring force proportional to its displacement, the force constant being d 2U 2 dx x x 0

27. 28. 29.

30.

The magnitude of force is maximum at : (A) x = 0 (B) x = + a

(C) x = – a

(D) no value of x

The body is in stable equilibrium at (A) x = 0 (B) x = +a

(C) x = – a

(D) both x = ± a

If body is at x = x0 where (i) x0 = 2a (ii) x0 = +a (iii) x0 = – a. If it is displaced slightly towards right, it will experience restoring force in (A) all the three cases (B) case (ii) only (C) case (iii) only (D) cases (i) and (ii) only. Match the statements in Column with the results in Column and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the OMR. (a) (b)

Column – I Work done by ideal gas during free expansion A wedge block system is as shown in the fig. The wedge lying on horizontal surface is accelerated to right by a horizontal force F. All surfaces are smooth. Work done by normal reaction exerted by wedge on block in any

Column – II (P) (Q)

zero non zero

time interval is (c)

(d)

Two identical conducting spheres of radius 'a' are separated (R) negative by a distance 'b' (b>>a). Both spheres carry equal and opposite charge. Net electrostatic potential energy of system of both spheres is A uniform cylinder lies over a rough horizontal platform. The (S) positive platform is accelerated horizontally as shown with acceleration a. The cylinder does not slip over the platform.The work done by the force of friction on the cylinder w.r.t ground in any time interval is

RESONANCE

5

31.

A particle is moving with speed v = 2t2 on the circumference of circle of radius R. Match the quantities given in column-I with corresponding results in column-II Column-I

Column-II

(A) Magnitude of tangential acceleration of particle (B) Magnitude of Centripetal acceleration of particle (C) Magnitude of angular speed of particle with respect to centre of circle (D) Angle between the total acceleration vector and centripetal acceleration vector of particle 32.

33.

(p) decreases with time. (q) increases with time (r) remains constant (s) depends on the value of radius R

In column-I condition on velocity, force and acceleration of a particle is given. Resultant motion is described in column-II. u = initial velocity, F = resultant force and v = instantaneous velocity.. Column-I Column-II (A) u F 0 and F = constant (p) path will be circular path (B) u F 0 and F = constant (q) speed will increase (C) v F 0 all the time and | F | = constant (r) path will be straight line and the particle always remains in one plane. (D) u 2 ˆi 3 ˆj and acceleration at all time a 6 ˆi 9 ˆj (s) path will be parabolic Each situation in column I gives graph of a particle moving in circular path. The variables , and t represent angular speed (at any time t) , angular displacement (in time t) and time respectively. Column gives certain resulting interpretation. Match the graphs in column with statements in column and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the OMR.

(A)

(p) Angular acceleration of particle is uniform

2

(B)

(q) Angular acceleration of particle is non-uniform 2

- graph

(C)

(r) Angular acceleration of particle is directly proportional to t. t - t graph

(D) t

2

(s) Angular acceleration of particle is directly proportional to .

2

- t graph

RESONANCE

6

34.

Net force on a system of particles in ground frame is zero. In each situation of column-I a statement is given regarding this system. Match the statements in column-I with the results in column-II. Column-I Column-II (A) Acceleration of centre of mass of system (p) is constant from ground frame (B) Net momentum of system from ground frame. (q) is zero (C) Net momentum of system from frame of centre (r) may be zero of mass of system (D) K.E. of system from frame of centre of mass (s) may be constant of system

35.

STATEMENT-1 : The sum of potential and kinetic energy for a system of moving objects is conserved only when no net external force acts on the objects STATEMENT-2 : If no nonconservative force acts on a system of objects, the work done by external forces on a system of objects is equal to change in potential energy plus change in kinetic energy of the system. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

36.

STATEMENT-1 : One end of ideal massless spring is connected to fixed vertical wall and other end to a block of mass m initially at rest on smooth horizontal surface. The spring is initially in natural length. Now a horizontal force F acts on block as shown. Then the maximum extension in spring is equal to maximum compression in spring. STATEMENT-2 : To compress and to expand an ideal unstretched spring by equal amount, same work is to be done on spring.

37.

STATEMENT-1 : For a particle moving in a circular path, if direction of angular velocity and angular acceleration is same, then angle between its velocity vector and acceleration vector increases. STATEMENT-2 : For a particle moving in a circular path with speed increasing at constant rate, the centripetal acceleration keeps on increasing (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True.

38.

STATEMENT-1 : A cyclist is cycling on a rough horizontal circular track with increasing speed. Then the net frictional force on cycle is always directed towards centre of the circular track. STATEMENT-2 : For a particle moving in a circle, component of its acceleration towards centre, that is, centripetal acceleration should exist (except when speed is zero instantaneously). (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

SUBJECTIVE QUESTIONS 39.

A ring of mass m can slide over a smooth vertical rod. The ring is connected to a spring of force constant K =

4 mg where 2 R is the natural length of the R

spring. The other end of the spring is fixed to the ground at a horizontal distance 2 R from the base of the rod. The mass is released at a height of 1.5 R from ground. (a) calculate the work done by the spring. (b) calculate the velocity of the ring as it reaches the ground.

RESONANCE

7

40.

A particle is being acted upon by one dimensional conservative force. In the F–x curve shown, four points A, B, C, D are marked on the curve. (a) State which type of equilibrium is the particle in at these positions. (b) Is the particle in equilibrium at all these points?

41.

A particle of mass 2kg starts to move at position x = 0 and time t = 0 under the action of force F= (10 + 4x) N along the x-axis on a frictionless horizontal track. Find the power delivered by the force in watts at the instant the particle has moved by the distance 5m.

42.

A rod AB is moving on a fixed circle of radius R with constant velocity ‘v’ as shown in figure. P is the point of 3R from centre of the circle. 5 The velocity of the rod is perpendicular to the rod and the rod is always parallel to the diameter CD.

intersection of the rod and the circle. At an instant the rod is at a distance x =

(a) Find the speed of point of intersection P. (b) Find the angular speed of point of intersection P with respect to centre of the circle. 43.

The block of mass m initially at x = 0 is acted upon by a horizontal force F = a bx2(where a > mg), as shown in the figure. The co-efficient of friction between the surfaces of contact is . The net work done on the block is zero, if the block travels a distance of ______.

1. 8. 15. 22. 29. 30. 32. 34.

D 2. A 3. C A 9. C 10. D B 16. A 17. C A,D 23. B,C 24. B D (A) p (B) q,s (C) q,s (D) q,s (A) r (B) q,s (C) p (D) q,r (A) p,q (B) p,r (C) p,q (D) r,s

Answer Key (Revision Test - 04)

39. 40.

41.

4. 11. 18. 25.

B C D A

5. 12. 19. 26.

C B D D

6. 13. 20. 27.

A D A A

31. 33. 35.

(A) q (B) q, s (C) q, s (D) p, s (A) q,s (B) p (C) p (D) q,r D 36. D 37. D

7. D 14. B 21.A,B,C,D 28. B

38.

D

mg R , 2 gR 2

(a)

Point

(b)

A No equilibrium B Unstable equilibrium C Stable equilibrium D Neutral equilibrium No, point A, F 0 i.e. particle is not in equilibrium

300

42.

(a)VP =

5 V 4

(b)

=

VP 5V = R 4R

43.

x = [3(a – mg)/b]½

Solution will be provided with next revision test.

RESONANCE

8

REVISION TEST - 05 Course : VIJAY (R) TOPIC : CENTER OF MASS Time : 3 Hrs.

Max. Marks : 129

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative marking). 2. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 3. For each correct answer in match the column 6 marks (with no negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking). 5. For each correct subjective question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

From the circular disc of radius 4 R two small disc of radius R are cut off. The centre of mass of the new structure will be : (Centre of lower circular cavity lies on x-axis and centre of upper circular cavity lies on y-axis) R R (A) ˆi ˆj 5 5

2.

(B) ˆi

R ˆR j 5 5

(C) ˆi

R ˆR j 5 5

(D)

3R ˆ ˆ ( i j) 14

The centre of mass of a non uniform rod of length L whose mass per unit length varies as k.x 2 where k is a constant & x is the distance of any point on rod from its one end, is (from the same end) L k 3 1 3k (A) L (B) L (C) (D) L 4 4 L Two semicircular rings of linear mass densities and 2 and of radius ‘R’ each are joined to form a complete ring. The distance of the center of the mass of complete ring from its centre is :

=

3.

3R 2R 3R (B) (C) (D) none of these 8 3 4 Both the blocks shown in the given arrangement are given together a horizontal velocity towards right. If acm be the subsequent acceleration of the centre of mass of the system of blocks, then acm equals (before sliding stops at all surfaces) (A) 0 m/s2 (B) 5/3 m/s2 (C) 7/3 m/s2 (D) 2 m/s2

(A) 4.

5.

6.

Two men ‘A’ and ‘B’ are standing on a plank. ‘B’ is at the middle of the plank and ‘A’ is the left end of the plank. System is initially at rest and masses are as shown in figure. ‘A’ and ‘B’ starts moving such that the position of ‘B’ remains fixed with respect to ground then‘A’ meets ‘B’. Then the point where A meets B is located at : (A) the middle of the plank (B) 30 cm from the left end of the plank (C) the right end of the plank (D) None of these Two balls of same mass are released simultaneously from heights h & 2h from the ground level. The balls collides with the floor & sticks to it. Then the velocity-time graph of centre of mass of the two balls is best represented by :

(A) 7.

8.

(B)

(C)

(D)

A cannon shell moving along a straight line bursts into two parts. Just after the burst one part moves with momentum 40 Ns making an angle 30º with the original line of motion. The minimum momentum of the other part of shell just after the burst is : (A) 0 Ns (B) 10 Ns (C) 20 Ns (D) 17.32 Ns Particle 'A' moves with speed 10 m/s in a frictionless circular fixed horizontal pipe of radius 5 m and strikes with 'B' of double mass that of A. Coefficient of restitution is 1/2 and particle 'A' starts its journey at t = 0. The time at which second collision occurs is : (A)

s 2

RESONANCE

(B)

2 s 3

(C)

5 s 2

(D) 4 s 1

9.

Three identical balls of mass m and radius R are placed on frictionless horizontal x-y plane. Ball A at (0, 0), Ball B at (4R, – 2 R) and ball C at (8R, – 2 2 R). Ball A is suddenly given an impulse P 2 mV ˆi . If collision between balls A and B is perfectly elastic while between B and C is perfectly inelastic, then the relative velocity of ball A with respect to ball C after a long time will be:

V ˆ V ˆ V ˆ V ˆ V ˆ 3V ˆ V ˆ 3V ˆ i i i i j j j j (B) (C) (D) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 A particle of mass m is moving along the x-axis with speed v when it collides with a particle of mass 2m initially at rest. After the collision, the first particle has come to rest, and the second particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the two pieces ? ( > 0) (A) Each piece moves with speed v. (B) Each piece moves with speed v/2. (C) One of the pieces moves with speed v/2, the other moves with speed greater than v/2 (D) Each piece moves with speed greater than v/2. (A)

10.

11.

A trolley filled with sand is moving with a velocity v on a smooth horizontal surface due to inertia. If the sand falls off at the rate of kg/sec, the velocity of the trolley as a function of time will be best represented by :

(A)

12.

(C)

(D)

In the fig. shown a cart moves on a smooth horizontal surface due to an external constant force of magnitude F. The initial mass of the cart is M0 and velocity is zero. Sand falls on to the cart with negligible velocity at constant rate kg/s and sticks to the cart. The velocity of the cart at time t is : (A)

13.

(B)

Ft M0 t

(B)

F t t e M0

(C)

Ft M0

(D)

Ft e t M0 t

In the figure, the block B of mass m starts from rest at the top of a wedge W of mass M. All surfaces are without friction. W can slide on the ground. B slides down onto the ground, moves along it with a speed v, has an elastic collision with the wall, and climbs back onto W. (A) B will reach the top of W again. (B) From the beginning, till the collision with the wall, the centre of mass of ‘B plus W’ is stationary. (C) After the collision, centre of mass of ‘B plus W’ moves with the horizontal component of velocity (D) When B reaches its highest position on W, the speed of W is

2mv m M

2mv . m M

Comprehension Figure shows block A of mass 0.2 kg sliding to the right over a frictionless elevated surface at a speed of 10 m/s. The block undergoes a collision with stationary block B, which is connected to a nondeformed spring of spring constant 1000 Nm–1. The coefficient of restitution between the blocks is 0.5. After the collision, block B oscillates in SHM with a period of 0.2 s, and block A slides off the left end of the elevated surface, landing a distance 'd' from the base of that surface after falling height 5m. (use 2 = 10; g = 10 m/s2) Assume that the spring does not affect the collision. 14. Mass of the block B is (A) 0.4 kg (B) 0.8 kg (C) 1 kg (D) 1.2 kg 15.

Amplitude of the SHM as being executed by block B-spring system, is

16.

(A) 2.5 10 cm (B) 10 cm The distance 'd' will be equal to (A) 2m (B) 2.5 m

RESONANCE

(C) 3 10 cm

(D) 5 10 cm

(C) 4m

(D) 6.25 m 2

Comprehension Figure shows an irregular wedge of mass m placed on a smooth horizontal surface. Part BC is rough.The other part of the wedge is smooth. 17.

What minimum velocity should be imparted to a small block of same mass m so that it may reach point B: (A) 2 gH

18.

(B)

2gH

(C) 2 g(H h)

(D) gh

The velocity of wedge when the block comes to rest (w.r.t. wedge) on part BC is :

(A) gH (B) g(H h (C) 2 gH (D) none of these If the coefficient of friction between the block and wedge is , and the block comes to rest with respect to wedge at a point D on the rough surface then BD will be H Hh h (A) (B) (C) (D) none of these Comprehension : A smooth rope of mass m and length L lies in a heap on a smooth horizontal floor, with one end attached to a block of mass M. The block is given a sudden kick and instantaneously acquires a horizontal velocity of magnitude V0 as shown in figure 1. As the block moves to right pulling the rope from heap, the rope being smooth, the heap remains at rest. At the instant block is at a distance x from point P as shown in figure-2 (P is a point on the rope which has just started to move at the given instant) , choose correct options for next three question. 20. The speed of block of mass M is 19.

mV0

(A) (M m x ) 21.

L

(C)

m3 L

V02 m (M x )3 L

(B)

V02 m (M x )3 L

mM 2 L

m 2 V0 m M (M x ) L

m4

(D)

V2

M2 V0 m m (M x ) L M2

0 (C) ML m (M x )3

V2

0 (D) L m (M x )3

L

L

The tension in rope at point P is (A)

23.

MV0 m (M x ) L

The magnitude of acceleration of block of mass M is (A)

22.

(B)

mM 2 L

V02 m (M x ) 2 L

(B)

m 2M L

V02 m (M x )2 L

(C)

m3 L

V02 m (M x ) 2 L

(D)

M3 L

V02 m (M x )2 L

In each situation of column-I a mass distribution is given and information regarding x and y-coordinate of centre of mass is given in column-II. Match the figures in column-I with corresponding information of centre of mass in column-II. Column-I Column-II (A) An equilateral triangular wire (p) xcm > 0 frame is made using three thin uniform rods of mass per unit lengths , 2 and 3 as shown (B) A square frame is made using four thin uniform rods of mass per unit length lengths , 2, 3 and 4 as shown

(q) ycm > 0

(C) A circular wire frame is made of two uniform semicircular wires of same radius and of mass per unit length and 2 as shown

(r)

(D) A circular wire frame is made of four uniform quarter circular wires of same radius and mass per unit length , 2, 3 and 4 as shown

(s) ycm < 0

RESONANCE

xcm < 0

3

25.

26.

27.

28. 29.

30.

31.

Two identical uniform solid spheres of mass m each approach each other with constant velocities such that net momentum of system of both spheres is zero. The speed of each sphere before collision is u. Both the spheres then collide. The condition of collision is given for each situation of column-I. In each situation of column- information regarding speed of sphere(s) is given after the collision is over. Match the condition of collision in column- with statements in column-. Column- Column- (A) Collision is perfectly elastic and head on (p) speed of both spheres after collision is u (B) Collision is perfectly elastic and oblique (q) velocity of both spheres after collision is different 1 (C) Coefficient of restitution is e = and (r) speed of both spheres after collision 2 collision is head on is same but less than u. 1 (D) Coefficient of restitution is e = and (s) speed of one sphere may be more than u. 2 collision is oblique STATEMENT-1 : Two spheres undergo a perfectly elastic collision. The kinetic energy of system of both spheres is always constant. [There is no external force on system of both spheres]. STATEMENT-2 : If net external force on a system is zero, the velocity of centre of mass remains constant. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True STATEMENT-1 : Non zero work has to be done on a moving particle to change its momentum. STATEMENT-2 : To change momentum of a particle a non zero net force should act on it. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True STATEMENT-1 : When a body collides elastically and head on with another identical stationary body on a frictionless surface, it losses all of its kinetic energy (No external forces on the system of the two bodies and no rotation of the bodies). STATEMENT-2 : In elastic collisions, only momentum is conserved. (a) If both assertion and reason are true and reason is the correct explanation of assertion (b) If both assertion and reason are true but reason is not the correct explanation of assertion. (c) If assertion is true but reason is false (d) If assertion is false but reason is true (A) a (B) b (C) c (D) d From a uniform square plate the shaded portions are removed as shown in figure. Find the coordinates of centre of mass of the remaining plate. X, Y axes and origin are shown in figure . In the figure shown two nonconducting blocks of A and B of mass ‘m’, 2m and charges – Q, 2Q respectively are attached at the two ends of a light spring of spring constant ‘k’. They are kept on a smooth horizontal surface. A and B are initially at rest and the spring is unstretched. Now a uniform electric field of intensity ‘E’ is switched on pointing towards right. Neglecting the electrostatic interaction between A and B find the maximum extension of the spring during the motion of the system. Also find the acceleration of ‘B’ at the moment of maximum extension in the spring A coordinate axis system taking x-axis as horizontal smooth floor is shown in figure. Two small balls of masses m and 3m attached with a string are released from some heights on y-axis as shown in figure. The balls may collide head on or obliquely. After a certain time mass m is at (9 cm, 20 cm) while mass 3m is 25 cm above the x axis and the strings is taut. The balls always remain in x-y plane. Find the length of string. A particle moving on a smooth horizontal surface strikes a stationary wall. The angle of strike is equal to the angle of rebound & is equal to 37° and 1 . Find the friction coefficient 5 X between wall and the particle in the form and fill value of X.: 10

the coefficient of restitution with wall is e =

37º 37º

////////////////////////////////////

24.

Answer Key (Revision Test - 05)

1.D 14. C

2. A 15. A

3. B 16. B

4. D 17. A

5. C 18. A

6. B 19. B

7. C 20. B

8. C 21. B

9. D 22. A

10. D 11. D 12. A 13. C,D 23. (A) q,r (B) p,s (C) p,s (D) p,s

8QE 55a 49a , 29. 3k 104 104 Solution will be provided with next revision test.

24. (A) p,q (B) p,q (C) q,r (D) q,r

RESONANCE

25. D

26. D

27. C

28.

30.

13 cm. 31. 5

4

REVISION TEST - 06 SUBJECT : PHYSICS COURSE : VIJAY (R) TOPIC : ROTATIONAL MOTION Time : 3 Hrs.

Max. Marks : 170

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative marking). 2. For each correct multipal choice question 3 marks (with 1 mark negative marking). 3. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking). 5. For each correct subjective question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

The moment of inertia of a thin sheet of mass M of the given shape about the specified axis is :

(A) 2.

7 Ma2 12

(B)

5 Ma2 12

(C)

R (B)

1 Ma2 12

(C)

2

R 2

(D)

R 4

A uniform ladder of length 5 m and mass 100 kg is in equilibrium between vertical smooth wall and rough horizontal surface. Find minimum friction co-efficient between floor and ladder for this equilibrium.

(A) 1/2 4.

(D)

A disc is hinged in a vertical plane about a point on its radius. What will be the distance of the hinge from the disc centre so that the period of its small oscillations under gravity is minimum? (A) R

3.

1 Ma2 3

(B) 3/4

(C) 1/3

(D) 2/3

Figure shows an arrangement of masses hanging from a ceiling. In equilibrium, each rod is horizontal, has negligible mass and extends three times as far to the right of the wire supporting it as to the left. If mass m4 is 48 kg then mass m1 is equal to :

m4 m3 m2 (A) 1 kg

RESONANCE

(B) 2 kg

(C) 3 kg

m1 (D) 4 kg

1

5.

A massless stick of length L is hinged at one end and a mass m attached to its other end. The stick is free to rotate in vertical plane about an fixed horizontal axis passing through frictionless hinge. The stick is held in a horizontal position. At what distance x from the hinge should a second mass M = m be attached to the stick, so that stick falls as fast as possible when released from rest. (A)

6.

(C) ( 2 1) L

3L

(D) ( 3 1) L

Two identical discs of mass m and radius r are arranged as shown in the figure. If is the angular acceleration of the lower disc and acm is acceleration of centre of mass of the lower disc, then relation between acm, & r is :

(A) acm = 7.

(B)

2L

r

(B) acm = 2

r

(C) acm = r

(D) none of these

A uniform rod of length l rotating with an angular velocity , while its centre moves with linear velocity v =

. If the end A of the rod is suddenly fixed, the 6

angular velocity of the rod will be : (A) 8.

(B)

3

(C)

2

(D)

2 3

A uniform disc of mass M and radius R is released from the shown position. PQ is a string, OP is a horizontal line, O is the centre of the disc and distance OP is R/2. Then tension in the string just after the disc is released will be :

(A) 9.

3 4

Mg 2

(B)

Mg 3

(C)

2Mg 3

(D) none of these

Mass m is connected with an ideal spring of natural length whose other end is fixed on a smooth horizontal table. Initially spring is in its natural length . Mass m is given a velocity ‘v’ perpendicular to the spring and released. The velocity perpendicular to the spring when its length is + x, will be

(A)

2v x

RESONANCE

(B)

2v 2 x

(C)

v x

(D) zero

2

10.

A uniform cubical solid block of side a moving with velocity v on a horizontal smooth plane as shown. It hits a fixed ridge at point O. The angular speed of the block just after it hits 'O' is

(A) 11.

v 3a

(C)

3v 2a

(D)

3v 4a

(B) r

(C) 3 r/2

(D) 2

Determine the acceleration a of the supporting surface required to keep the centre G of the circular pipe in a fixed position during the motion. No slipping takes place between pipe and its support.

(A) g sin 13.

v 2a

A uniform circular disc placed on a horizontal rough surface has initially a velocity v0 and an angular velocity 0 as shown in the figure. The disc comes to rest after moving some distance in the direction of motion. Then v0/0 is : (A) r/2

12.

(B)

(B) 2g sin

(C)

g sin 2

(D) 2 g sin

A solid sphere of mass m and radius r is gently placed on a conveyer belt moving with constant velocity V. If the coefficient of friction between the belt and sphere is

2 , the distance travelled by the centre of 7

the sphere before it starts pure rolling is

V2 (A) 7g 14.

2V 2 (C) 5g

2V 2 (D)

7g

A solid homogeneous cylinder of height h and base radius r is kept vertically on a conveyer belt moving horizontally with an increasing velocity v = a + bt2. If the cylinder is not allowed to slip then the time when the cylinder is about to topple, will be equal to (A)

15.

2V 2 (B) 49 g

rg bh

(B)

2 rg bh

(C)

2 bg rh

rg (D) 2 bh

A ring of mass m and radius R rolls on a horizontal rough surface without slipping due to an applied force ‘F’. The friction force acting on ring is :

(A)

F 3

RESONANCE

(B)

2F 3

(C)

F 4

(D) Zero

3

16.

A uniform disc of mass 2kg and radius 1m is mounted on an axle supported on fixed frictionless bearings. A light cord is wrapped around the rim of the disc and mass of 1kg is tied to the free end. If it is released from rest, (A) the tension in the cord is 5N (B) in first 4 seconds the angular displacement of the disc is 40 rad. (C) the work done by the torque on the disc in first 4 sec. is 200J (D) the increase in the kinetic energy of the disc in the first 4 seconds is 200J.

17.

Which of the following statements is/are true (A) work done by kinetic friction on an object may be positive. (B) A rigid body rolls up an inclined plane without sliding. The friction force on it will be upwards. (only contact force and gravitational force is acting) (C) A rigid body rolls down an inclined plane without sliding. The friction force on it will be upwards. (only contact force and gravitational force is acting) (D) A rigid body is left from rest from the top of a rough inclined plane. It moves down the plane with slipping. The friction force on it will be upwards.

Comprehension # 1 A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown. Assume tension in the lower part of chain negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Negelect friction within cycle parts & the rolling friction.

Chain upper part

F=100N

Gear 16cm

r=4cm

Sprocket Disc Wheel R=35cm

18.

19.

20.

21.

22.

The tension in the upper portion of the chain is equal to (A) 100 N (B) 120 N (C) 160 N

(D) 240 N

Net torque on the rear wheel of the bicycle is equal to (A) zero (B) 16 N-m (C) 6.4 N-m

(D) 4.8 N-m

The power delivered by the cyclist is equal to (A) 280 W (B) 100 W

(C) 64 W

(D) 32 W

The speed of the bicycle is : (A) 6.4 m/s (B) 3.5 m/s

(C) 2.8 m/s

(D) 5.6 m/s

The net force of the friction on the rear wheel due to the road is : (A) 100 N (B) 62 N (C) 32.6 N

(D) 18.3 N

Comprehension # 2 A square frame of mass m is made of four identical uniform rods of length L each. This frame is placed on an inclined plane such that one of its diagonals is parallel to the inclined plane as shown in figure, and is released.

RESONANCE

4

23.

The moment of inertia of square frame about the axis of the frame is : (A)

24.

(B)

2mL2 3

(C)

4mL2 3

(D)

mL2 12

The frictional force acting on the frame just after the release of the frame assuming that it does not slide is : (A)

25.

mL2 3

mg sin 3

(B)

2mg sin 7

(C)

3mg sin 5

(D)

2mg sin 5

The acceleration of the center of square frame just after the release of the frame assuming that it does not slide is : (A)

g sin 3

(B)

2 g sin 7

(C)

3 g sin 5

(D)

2 g sin 5

Comprehension # 3 A horizontal uniform rod of mass 'm' has its left end hinged to the fixed incline plane, while its right end rests on the top of a uniform cylinder of mass 'm' which in turn is at rest on the fixed inclined plane as shown. The coefficient of friction between the cylinder and rod, and between the cylinder and inclined plane, is sufficient to keep the cylinder at rest.

26.

The magnitude of normal reaction exerted by the rod on the cylinder is (A)

27.

mg 4

mg 3

(C)

mg 2

(D)

2 mg 3

The ratio of magnitude of frictional force on the cylinder due to the rod and the magnitude of frictional force on the cylinder due to the inclined plane is: (A) 1 : 1

28.

(B)

(B) 2 : 3

(C) 2 : 1

(D)

2 :1

The magnitude of normal reaction exerted by the inclined plane on the cylinder is: (A) mg

(B)

3 mg 2

(C) 2mg

(D)

5 mg 4

29.

STATEMENT-1 : A disc rolls without slipping on a fixed rough horizontal surface. Then there is no point on the disc whose velocity is in vertical direction. STATEMENT-2 : Rolling motion can be taken as combination of translation and rotation. Due to the translational part of motion a velocity (translational component) exist in horizontal direction for any point on the disc rolling on a fixed rough horizontal surface. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True.

30.

STATEMENT-1 : A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity. Then the acceleration of lowest point on the disc is zero. STATEMENT-2 : For a rigid disc rolling without slipping on a fixed rough horizontal surface, the velocity of the lowest point on the disc is always zero. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True.

RESONANCE

5

31.

STATEMENT-1 : A uniform cubical block(of side a) undergoes translational motion on a smooth horizontal surface under action of horizontal force F as shown. Under the given condition, the horizontal surface exerts normal reaction non-uniformly on lower surface of the block.

STATEMENT-2 : For the cubical block given in statement-1, the horizontal force F has tendency to rotate the cube about its centre in clockwise sense. Hence, the lower right edge of cube presses the horizontal surface harder in comparision to the force exerted by lower left edge of cube on horizontal surface. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. 32.

STATEMENT-1 : A homogeneous rectangular brick lies at rest on a fixed rough inclined plane as shown. Then the right half of the brick exerts greater force on the inclined plane as compared to left half of the brick.

STATEMENT-2 : For brick in situation of statement-1 to be at rest, the net moment of all forces about its centre of mass should be zero. Moment of force on brick due to its weight about centre of mass is zero. The moment of force due to friction on brick about its centre of mass has tendency to rotate the brick in clockwise sense. Hence the right half of the brick presses the inclined plane more in comparision to the left half of the brick. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True 33.

STATEMENT-1 : A body is purely rolling (rolling without slipping). The velocity of point of contact (of body) must be zero with respect to ground. STATEMENT-2 : By definition, pure rolling of a body occurs when velocity of its point of contact is zero relative to the surface on which it rolls. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

34.

Find out the moment of inertia of the following structure (written as thin uniform rods of mass per unit length .

RESONANCE

) about axis AB made of

6

35.

A circular hole of radius R/2 is cut from a thin uniform circular plate of radius R as shown (O is the centre of the circular plate). If the mass of the remaining plate is M, then find the moment of inertia of the plate about an axis through O perpendicular to plane of the plate ?

36.

In figure the uniform gate weighs 300 N and is 3 m wide & 2 m high. It is supported by a hinge at the bottom left corner and a horizontal cable at the top left corner, as shown. Find : (a)

the tension in the cable and

(b)

the force that the hinge exerts on the gate (magnitude & direction).

37.

The arrangement shown in figure consists of two identical uniform solid cylinders, each of mass m, on which two light threads are wound symmetrically. Find the tension of each thread in the process of motion. The friction in the axle of the upper cylinder is assumed to be absent.

38.

Two steel ball of equal diameter are connected by a rigid bar of negligible weight as shown and are dropped in the horizontal position from height h above the heavy steel and brass base plates. If the coefficient of restitution between the ball and steel base is 0.6 and that between the other ball and the brass base is 0.4. The angular velocity of the bar immediately after rebound is _______. Assume the two impacts are simultaneous. (g = 10 m/s 2)

39.

A ball of diameter d rolls without slipping along a horizontal smooth table top with constant speed v. The ball rolls off the edge falling to the floor a vertical distance h below. While in air the ball makes _______ revolutions.

40.

In the figure A & B are two blocks of mass 4 kg & 2 kg respectively attached to the two ends of a light string passing over a disc C of mass 40 kg and radius 0.1 m. The disc is free to rotate about a fixed horizontal axes, coinciding with its own axis. The system is released from rest and the string does not slip over the disc. Find:

(i) (ii) (iii)

the linear acceleration of mass B. the number of revolutions made by the disc at the end of 10 sec. from the start. the tension in the string segment supporting the block A. (g = 10 m/s 2)

RESONANCE

7

41.

A rigid cube ABCDEFGH is in motion. At a certain moment, face ABCD is vertical, and the velocities of vertices A and D are directed vertically downward and equal to v. At the same moment, the speed of point H equals 2v. What point of the cube has the maximum speed at that moment ? What is that speed ?

42.

A uniform ball of radius R rolls without slipping between two rails such that the horizontal distance is d between two contact points of the rail to the ball. If R=10cm, d=16cm and the angular velocity is 5rad/s velocity of centre of mass of the ball equals_____ [Pure rolling]

43.

A disk of mass M and radius R has a spring of constant k attached to its centre, the other end of the spring being fixed to a vertical wall. If the disk rolls without slipping on a level floor, how far to the right does the centre of mass move, if initially the spring was unstretched and the angular speed of the disk was o.

ANSWER KEY 1. 8. 15. 21. 28. 34.

A C D B B 13 3

2. 9. 16. 22. 29. 35.

37.

T = 1/10 mg

40.

(i) 10/13 m/s2 (ii) 5000/26 p (iii) 480/13 N

42.

0.3 m/sec

RESONANCE

B 3. C 10. A,B,C,D D 23. A B 30. 13/24 MR2 38.

43.

D D 17. 24. D 36.

0.28 rad/sec

4. A 5. C 6. B 11. A 12. A 13. A A,B,C,D 18. C 19. A D 25. C 26. C 27. 31. C 32. A 33. D (a) T = 225N, (b) FX = 225N, FY = 300N 39.

v d 41.

7. 14. 20. A

C A C

2h g vmax = 2L 2 L2 =

5 L

R o3m/2k)

8

REVISION TEST - 07 Course : VIJAY (R) TOPIC : ELECTROSTATICS Time : 3 Hrs.

Max. Marks : 170

Instructions : 1. For each correct Single choice question 3 marks (with 1 mark negative marking). 2. For each correct Multiple choice question 4 marks (with 1 mark negative marking). 3. For each correct answer in Comprehension 4 marks (with 1 mark negative marking). 4. For each correct Assertion/Reason question 3 marks (with 1 mark negative marking). 5. For each correct Subjective question 6 marks (with no negative marking). 6. For each correct Match the column question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

Five styrofoam balls are suspended from insulating threads. Several experiments are performed on the balls and the following observations are made : (i) Ball A repels C and attracts B. (ii) Ball D attracts B and has no effect on E. (iii) A negatively charged rod attracts both A and E. An electrically neutral styrofoam ball gets attracted if placed nearby a charged body due to induced charge. What are the charges, if any, on each ball ? A B C A B C D E (A) + – + 0 + (B) + – + + 0 D E (C) + – + 0 0 (D) – + – 0 0

2.

Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges of Q and – 3Q. They are suspended from two strings of same length fixed to points at the same horizontal level, but distant from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is (A) 2 (B) 3 (C) 1.5 (D) None of these

3.

A large sheet carries uniform surface charge density . A rod of length 2 has a linear charge density on one half and - on the second half. The rod is hinged at mid-point O and makes angle with the normal to the sheet. The electric force experienced by the rod is & (A) 0

4.

(B)

2 sin 2 0

(C)

2 sin (D) None of these 0

AB and CD are uniform line charges of infinite length having charge density 1 and 2 and lying along the z axis and y–axis respectively. The force between them depends on the perpendicular distance between them, 'r' as, F

(A) 0

RESONANCE

1. 2 2 0r n

, then the value of n is :

(B) 1/2

(C) 1

(D) 2

1

5.

A point charge – q is revolving in a circle of radius ' r ' around a fixed infinite line charge with positive charge per unit length. Now the point charge is shifted and it revolves in a circle of radius ' 2 r '. Then: (A) work done by all forces is zero (B) work done by electrical force is zero (C) work done by external force is zero (D) work done by all forces cannot be zero

6.

A ring carries a uniform linear charge density on one half and the linear charge density of same magnitude but opposite sign on the other half. (A) the component of electric field along the axis at all points on the axis is zero (B) the electric field along the axis and on the axis is zero only at the centre (C) the resultant field at the centre is zero (D) the resultant field at all points on the axis is zero. Two concentric rings, one of radius R and total charge +Q and the second of radius

7.

2R and total charge 8 Q, lie in x-y plane (i.e., z = 0 plane). The common centre of rings lies at origin and the common axis coincides with z-axis. The charge is uniformly distributed on both rings. At what distance from origin is the net electric field on z-axis zero. & (A) 8.

R 2

R (C)

2

2 2

(D)

2R

If the electric potential of the inner shell is 10 volt & that of the outer shell is 5 volt, then the potential at the centre will be: (the shells are uniformly charged)

(A) 10 volt 9.

R (B)

(B) 5 volt

(C) 15 volt

Find out work done by electric field in shifting a point charge

(D) 0 4 2 C from point P to S which are shown in 27

the figure :

(A) 10.

100 J 3

(B)

200 J 3

(C) 100 J

(D) 200 J

Figure shows three circular arcs, each of radius R and total charge as indicated. The net elecric potential at the centre of curvature is :

+Q 45° –2Q

•

30°

R +3Q

Q (A) 2 R 0

RESONANCE

Q (B) 4 R 0

2Q (C) R 0

Q (D) R 0

2

11.

Figure shows a solid hemisphere with a charge of 5 nC distributed uniformly through its volume. The hemisphere lies on a plane and point P is located on the plane, along a radial line from the centre of curvature at distance 15 cm. The electric potential at point P due to the hemisphere, is : P 15cm

(A) 150 V 12.

(B) 300 V

(B)

Qq / 4 0 mr

(C) 0

Qqm / 4 0 r

(D) cannot determine

A point mass ' m ' and charge ' q ' is projected with a velocity v towards a stationary charge Q0 from a distance of 2 m. The closest distance that q can approach is: [ k = 1/4 0 ]

(A) 14.

(D) 600 V

A charged particle of charge ‘Q’ is held fixed and another charged particle of mass ‘m’ and charge ‘q’ (of the same sign) is released from a distance ‘r’. The impulse of the force exerted by the external agent on the fixed charge by the time distance between ‘Q’ and ‘q’ becomes 2r is (A)

13.

(C) 450 V

mv 2 kqQ0 kQ0 q

(B)

kQ 0 2

mv k qQ 0

(C)

kQ 0 mv 2 k qQ 0

(D)

kQ 0 mv 2 k qQ 0

Two smooth spherical non conducting shells each of radius R having uniformly distributed charge Q & Q on their surfaces are released on a smooth non-conducting surface when the distance between their centres is 5 R. The mass of A is m and that of B is 2 m. The speed of A just before A and B collide

1 is: [Neglect gravitational interaction] (take K = 4 ) 0

(A) 15.

2 kQ 2 5 mR

(B)

4 kQ 2 5 mR

(C)

8 kQ 2 5 mR

(D)

16 kQ 2 5 mR

Four charges are rigidly fixed along the Y axis as shown. A positive charge approaches the system along the X axis with initial speed just enough to cross the origin. Then its total energy at the origin is

(A) zero 16.

(B) positive (C) negative (D) data insufficient p ˆ Two short dipoles p kˆ & k are located at (0, 0, 0) & (1 m, 0, 2 m) respectively. The resultant electric 2 field due to the two dipoles at the point (1 m, 0, 0) is : (A)

9p kˆ 32 0

RESONANCE

(B)

7p kˆ 32 0

(C)

7p kˆ 32 0

(D) none of these

3

17.

Total electric force on an electric dipole placed in an electric field of a point charge is: (A) always zero (B) never zero (C) zero when mid point of dipole coincides with the point charge (D) zero when dipole axis is along any electric line of force.

18.

A dipole of dipole moment p is kept at the centre of a ring of radius R and charge Q. The dipole moment has direction along the axis of the ring. The resultant force on the ring due to the dipole is: kPQ 2kPQ (A) zero (B) 3 (C) R R3 (D)

19.

kPQ

only if the charge is uniformly distributed on the ring

R3

For a system of two dipoles P1 and P2 as shown in the figure (both are at origin and perpendicular to each other along x and y axes respectively) (A) Work done in taking electron from P to R on QPR = 0 (B)

tan

(P1 P2 ) = 2 (P P ) 1 2

(C) tan

r

(P1 P2 ) = 2(P P ) 1 2

(D)

E .d r =

P1 P2 4 2 0 r 2

(P1 and P2 denotes magnitudes of P1 and P2 and r is quite large in comparison to dimensions of

dipoles, E is resultant electric field and QPR is a quarter of circle whose centre is at O) 20.

Two infinitely large charged planes having uniform surface charge density + and – are placed along x-y plane and yz plane respectively as shown in the figure. Then the nature of electric lines of forces in x-z plane is given by : z –

+

z

z

z

x (A)

21.

x

x (B)

z

x (C)

x (D)

Two equipotential spherical surfaces having potential 20 V and 0 V are as shown in figure. There is no charge anywhere in space except on the surface of both the spheres. Then which of the following figure represents the nature of electric field in region between the spherical surfaces by electric lines of forces. 0V

20V

(A)

RESONANCE

(B)

(C)

(D)

4

22.

A ring of radius R is placed in the plane with its centre at origin and its axis along the x-axis and having uniformly distributed positive charge. A ring of radius r ( 0. Neglect gravity. Find the time period.

38.

A point charge – q revolves around a fixed charge +Q in elliptical orbit. The minimum and maximum distance of – q from Q are r1 and r2 respectively. The mass of revolving particle is m. Qq > 0 and assume no gravitational effects. Find the angular momentum of q about Q .

39.

Find the magnitude of uniform electric field E in N/C (direction shown in figure) if an electron entering with velocity 100m/s making 30° comes out making 60° (see m figure), after a time numerically equal to of electron. e

40.

A solid sphere of radius ‘R’ is uniformly charged with charge density in its volume. A spherical cavity of radius

R is made in the sphere as shown in the figure. Find the electric 2

potential at the centre of the sphere. 41.

The arrangement shown consists of three elements

1. 2.

a thin rod of charge – 3.0 C that forms a full circle of radius 6.0 cm. a second thin rod of charge 2.0 C that forms a circular arc of radius 4.0 cm and concentric with the full circle, subtending an angle of 90° at the centre of the full circle. 3. an electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude 1.28 × 10–21 C-m. Find the net electric potential in volts at the centre.

42.

Electric field in a region is given by E 4 x ˆi 6 y ˆj . Then find the charge enclosed in the cube of side 1m oriented as shown in the diagram.

43.

A conducting sphere of radius R has two spherical cavities of radius a and b. The cavities have charges qa & qb respectively at their centres. ‘A’ is the centre of the sphere and ‘B’ is the centre of the cavity of radius ‘b’. Find : (i) electric field & electrical potential at (a) r (distance from A)> R, (b) r (distance from B)< b (ii) surface charge densities on the surface of radius R, radius a & radius b. (iii) What is the force on qa & qb?

RESONANCE

7

MATCH THE COLUMN 44.

Column gives a situation in which point charge(s) are placed at different position with respect to a uncharged thick conducting spherical shell. Column gives resulting effect. Match the figures in Column with the statements in Column . Column Column positive point charge q is placed at centre of shell

q

(A)

positive point charge q is placed inside gap of shell, but not at centre

q

(B)

(p)

charge is induced on inner surface of shell and is distributed uniformly

(q)

charge is induced on inner surface of shell and is distributed non-uniformly

(r)

charge is induced on outer surface of shell and is distributed uniformly

(s)

charge is induced on outer surface of shell and is distributed non-uniformly

q positive point charge q is placed outside the shell

(C)

(D)

A NS W ER S 1. 8. 15. 22. 29.

C A B C A

2. 9. 16. 23. 30.

C A B C B

3. 10. 17. 24. 31.

A A B B D

4. 11. 18. 25. 32.

A B B C D

5. 12. 19. 26. 33.

A B C C A

6. 13. 20. 27.

A B C AC

7. D 14. A 21. D 28. ABCD

6 q2

34.

4 0 a 2

35.

(a) 60º (b) mg +

kq1q2 2

stationary & q1q2 =

3 mg , mg . q1 & q2 should have unlike charges for the beads to remain

mg 2 k

md2 0 4 q

36.

4

37.

2

41.

0

42.

q = 2 0

38.

43.

Q q m r1 r2 2 0 (r1 r2 ) (i) (a)

Kqb Kqb Kqb K(qa qb ) – + ; E= 2 b r R r (A) p,r (B) q,r (C) s (D) q,s

(b) v = 44.

(c)

RESONANCE

v=

39.

100

5R 2 12 0

40.

K ( q a qb ) K(qa qb ) ; E= r r2

(ii) R =

qa qb 4R

2

, a =

qa 4 a

2

, b =

qb 4 b 2

(iii)

0

8

REVISION TEST - 08 Course : VIJAY (R) TOPIC : CAPACITANCE & CURRENT ELECTRICITY Time : 3 Hrs.

Max. Marks : 150

Instructions : 1. For each correct Single choice question 3 marks (with 1 mark negative marking). 2. For each correct Multiple choice question 3 marks (with 1 mark negative marking). 3. For each correct answer in Comprehension 4 marks (with 1 mark negative marking). 4. For each correct Assertion/Reason question 3 marks (with 1 mark negative marking). 5. For each correct Subjective question 6 marks (with no negative marking). 6. For each correct Match the column question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

The capacitance of a parallel plate capacitor will increase if: (A) a battery is connected to it (B) distance between the plates is increased (C) one plate is displaced parallel to itself by distance less than its length (D) none of these.

2.

A,B,C,D are large conducting plates kept parallel to each other. A and D are fixed. Plates B and C, connected to each other by a rigid conducting rod can slide over frictionless rails as shown. Initially the distance between plates A and B is same as that between plates C and D. If now the rod (along with plates B and C) is slightly moved towards right, the capacitance between the terminals 1 and 2. (A) remains unchanged (B) increases (C) decreases (D) nothing can be said

3.

The equivalent capacitance between x and y is:

(A) 4.

(B)

7 F 6

(C)

8 F 3

(D) 4 F

In the figure initial status of capacitor and their connection is shown. Which of the following is incorrect about this circuit :

(A) (B) (C) (D) 5.

5 F 6

Final charge on each capacitor will be zero Final total electrical energy of the capacitors will be zero Total charge flown from A to D is 30µC Total charge flown from A to D is – 30µC

A parallel plate capacitor of capacitance C (without dielectrics) is filled by dielectric slabs as shown in figure. Then the new capacitance of the capacitor is:

(A) 3.9 C

RESONANCE

(B) 4 C

(C) 2.4 C

(D) 3 C

1

6.

In the figure shown P1 and P2 are two conducting plates having charges of equal magnitude and opposite sign. Two dielectrics of dielectric constant K1 and K2 fill the space between the plates as shown in the figure. The ratio of electrical energy in 1st dielectric to that in the 2nd dielectric is (A) 1 : 1 (C) K2 : K1

7.

In the circuit shown the capacitor is initially uncharged. The charge passed through an imaginary circular loop parallel to the plates (also circular) and having the area equal to half of the area of the plates, in one time constant is:

(A) 0.63 C 8.

(B) K1 : K2 (D) K22 : K12

(B) 0.37 C

(C)

C

(D) zero

2

A graph between current & time during charging of a capacitor by a battery in series with a resistor is shown. The graphs are drawn for two circuits. R1, R2, C1, C2 and V1V2 are the values of resistance, capacitance and EMF of the cell in the two circuits. If only two parameters (out of resistance, capacitance, EMF) are different in the two circuits. What is /are the correct option(s) (A) V1 = V2; R1 > R2, C1> C2 (C) V1 < V2, R1< R2, C1 = C2

(B) V1 > V2, R1 > R2 ; C1 = C2 (D) V1 < V2, C1< C2, R1 = R2

9.

In the figure a capacitor of capacitance 2µF is connected to a cell of emf 20 volt. The plates of the capacitor are drawn apart slowly to double the distance between them. The work done by the external agent on the plates is : (A) – 200 µJ (B) 200 µJ (C) 400 µJ (D) – 400 µJ

10.

The plates S and T of an uncharged parallel plate capacitor are connected across a battery. The battery is then disconnected and the charged plates are now connected in a system as shown in the figure. The system shown is in equilibrium. All the strings and spring are insulating and massless. The magnitude of charge on one of the capacitor plates is: [ Area of plates = A ]

(A) 11.

2 m g A 0

(B)

4 m g A 0 k

(C)

m g A 0

(D)

2 m g A 0 k

In the capacitor discharge formula q = q0 e–t/ the symbol represents : (A) the time it takes for C to loose q0/e charge. 1 (B) the time it takes for C to loose charge q0 1 e (C) the time it takes for C to loose essentially all of its initial charge. (D) none of the above.

12.

A uniform wire of resistance R is stretched uniformly n times & then cut to form five identical wires. These wires are arranged as shown in the figure. The effective resistance between A & B will be:

(A)

nR 5

RESONANCE

R

(B)

5n

2

(C)

n2 R 5

(D)

n2 R 2

2

Conductivity

(C) Conductivity

(D) Conductivity

Resistivity

(B)

Resistivity

(A)

Resistivity

Which graph best represent the relationship between conductivity and resistivity for a solid ? Resistivity

13.

Conductivity

14.

A battery of internal resistance 2 is connected to a variable resistor whose value can vary from 4 to 10 . The resistance is initially set at 4 If the resistance is now increased then (A) power consumed by it will decrease (B) power consumed by it will increase (C) power consumed by it may increase or may decrease (D) power consumed will first increase then decrease.

15.

The resistance of each arm in the circuit shown in figure has same value. (i.e. R12 = R10 = R13 = R2O = R24 = ..... etc.). The ratio Q12/Q34 of the amounts of heat liberated per unit time in conductors 1-2 and 3-4 is : (A) 4 : 1 (B) 8 : 1 (C) 16 : 1 (D) none of these

16.

In the circuit shown the variable resistance X is to be adjusted such that the ideal ammeter reads the same in both the positions of the key, when connected independently to 1 and then to 2. The reading of the ammeter is 2A. If E = 10 V, then x is : (A) 5. (B) 20 (C) 50 (D) cannot be determined

17.

In the diagrams, all light bulbs are identical and all emf sources are ideal and identical. In which circuit (given in options) will each bulb glow with the same brightness as in the circuit shown ?

(A)

18.

19.

(B)

(C)

(D)

In the circuit shown in figure, the resistance of voltmeter is 6 K. The voltmeter reading will be : (A) 6V

(B) 5V

(C) 4V

(D) 3V

In a practical wheat stone bridge circuit as shown, when one more resistance of 100 is connected in parallel with unknown resistance ' x ', then ratio 1/2 become ' 2 '. 1 is balance length. AB is a uniform wire. Then value of ' x ' must be: copper strips (rk¡ csd h ifê;k¡ ) 100

x G

A 1

2 E

(A) 50

RESONANCE

(B) 100

B copper strips (rk¡ csd h ifê;k¡ )

r

(C) 200

(D) 400

3

MULTIPLE CHOICE QUESTIONS 20.

Charged particles with different charge to mass ratios are projected into the region of space between the plates of a parallel plate capacitor with velocities directed parallel to the plates. All particles have received their initial kinetic energy by passing the same potential difference V0. The potential difference across the capacitor plates is V, and the distance between the plates is d. If all the particles are projected from a point that is exactly in the middle of the distance between the plates and '' is the distance travelled (along the direction of initial velocity) by any particle before hitting any of the plate, then is dependent as (neglect the interaction among the particles and effect of induction) :

d

(A) V0 21.

(B)

q m

(C)

1

(D) d

V

Two capacitors C 1 & C 2 are charged to same potential V, but with opposite polarity as shown in fig. The switch S 1 & S 2 are then closed.

(A)P.d. across two capacitors are same & is given by

(C1 C 2 )V (C1 C 2 )

C1V (B)P.d. across two capacitors are same & is given by (C C ) 1 2

(C1 C 2 ) (C)Ratio of final energy to initial energy of the system is (C1 C 2 )

2

(C1 ) (D)Ratio of final energy to initial energy of the system is 2 (C1 C2 ) 22.

The figure shows, a graph of the current in a discharging circuit of a capacitor through a resistor of resistance 10 . (A) The initial potential difference across the capacitor is 100 volt.

1 (B) The capacitance of the capacitor is 10 n 2 F.. (C) The total heat produced in the circuit will be

500 joules. n2

(D) The thermal power in the resistor will decrease with a time constant 23.

1 second. 2 n2

In the figure a conductor of nonuniform cross-section is shown. A steady current flows in it. (A) The electric field at A is more than at B. (B) The electric field at B is more than at A. (C) The thermal power generated at A is more than at B in an element of small same width. (D) The thermal power generated at B is more than at A in an element of small same width.

RESONANCE

4

COMPREHENSION Comprehension The circuit contains ideal battery E and other elements arranged as shown. The capacitor is initially uncharged and switch S is closed at t = 0. (use e2 = 7.4)

24.

Time constant of the circuit is (A) 48 s (B) 28.8 s

(C) 72 s

(D) 120 s

25.

The potential difference across the capacitor in volts, after two time constants, is approximately : (A) 2 (B) 7.6 (C) 10.4 (D) 12

26.

The potential difference across resistor R1 after two time constants, is approximately : (A) 1.6 V (B) 7.6 V (C) 10 V (D) 12 V

27.

The potential difference across resistor R2 after two time constants, is : (A) 2V

(B) 7.6V

(C) 10V

(D) 12 V

Comprehension In the circuit shown below, the internal resistance of the cell is negligible. The distance of the slider from the left-hand end of the slide wire is . The graph shows the variation with of the current in the cell.

+

–

6.00 V d.c. 100 cm Slider

100 cm slider wire

R Cell

28.

29.

Centre zero milliammeter

The balance point is at length l that is equal to (A) 0 cm (B) 20 cm

(C) 30 cm

(D) 40 cm

E.M.F. of the cell is : (A) 0.98 V

(C) 1.86 V

(D) 2.00 V

(B) 1.20 V

ASSERTION / REASON 30.

STATEMENT-1 : A dielectric is inserted between the plates of an isolated fully-charged capacitor. The dielectric completely fills the space between the plates. The magnitude of electrostatic force on either metal plate decreases, as it was before the insertion of dielectric medium. STATEMENT-2 : Due to insertion of dielectric slab in an isolated parallel plate capacitor (the dielectric completely fills the space between the plates), the electrostatic potential energy of the capacitor decreases. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True.

RESONANCE

5

31.

STATEMENT-1 : When an external resistor of resistance R (connected across a cell of internal resistance r) is varied, power consumed by resistance R is maximum when R = r. STATEMENT-2 : Power consumed by a resistor of constant resistance R is maximum when current through it is maximum. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

SUBJECTIVE CHOICE QUESTIONS 32.

Find the equivalent capacitance between terminals ‘A’ and ‘B’. The letters have their usual meaning.

33.

Find the equivalent resistance of the circuit as shown in the figure between the junctions A and B. Each of the twelve wires have a resistance R ohms .

34.

(a)

In the circuit shown the resistance ‘R’ can be varied. Plot the graph of current through ‘R’ against R.

(b)

In the figure shown ‘R’ can be varied. Find the value of ‘R’ so that electric power consumed by it becomes maximum.

35.

Two potentiometer wires w1 and w2 of equal length connected to a battery of emf P and internal resistance ' r ' through two switches s 1 and s 2. A battery of emf is balanced on these potentiometer wires. If potentiometer wire w1 is of resistance 2r and balancing length is /2 when only s 1 is closed

2 , then find 3

and s 2 is open. On closing s 2 and opening s 1 the balancing length on w2 is found to be the resistance of potentiometer wire w2.

RESONANCE

6

MATCH THE COLUMN 36.

Column I gives physical quantities of a situation in which a current i passes through two rods I and II of equal length that are joined in series. The ratio of free electron density (n), resistivity () and cross-section area (A) of both are in ratio n1 : n2 = 2 : 1, 1 : 2 = 2 : 1 and A1 : A2 = 1 : 2 respectively. Column II gives corresponding results. Match the ratios in Column with the values in Column .

i A

B

C

Column

37.

Column

(A)

Drift velocity of free electron in rod Drift velocity of free electron in rod

(p) 0.5

(B)

Electric field in rod Electric field in rod

(q) 1

(C)

Potential difference across rod Potential difference across rod

(r) 2

(D)

Average time taken by free electron to move from A to B Average time taken by free electron to move from B to C

(s) 4

Match the readings of the voltmeter and ammeter respectively shown in the figures. Column Column

3

(a) 7V

24V

(P) 0V

3

7V

24V

(b)

V

7V

(Q) 20A

3 24V

(c)

7V

(d)

RESONANCE

(R) 0A

3 24V A

(S) 20 V

7

38.

Column I gives certain situations in which capacitance of a capacitor is changed by different means. Column II gives resulting effect under different conditions. Match the statements in column I with the corresponding statements in column II. Column I Column II (A) The plates of a plane parallel capacitor are (p) Increases if the capacitor is maintained slowly pulled apart. Then the magnitude of at constant charge. electric field intensity inside the capacitor. (B) The plates of a plane parallel plate capacitor (q) Decreases if the capacitor is are slowly pulled apart. Then the potential maintained at constant charge energy stored in the capacitor. (C) The capacitance of an air filled plane parallel (r) Increases if the capacitor is maintained plate capacitor on insertion of dielectric at constant potential difference. (D) A dielectric slab is inserted inside an air (s) Decreases if the capacitor is maintained filled plane parallel plate capacitor. The at constant potential difference. potential energy stored in the capacitor.

39.

Two identical capacitors are connected in series, and the combination is connected with a battery, as shown. Some changes in the capacitor 1 are now made independently after the steady state is achieved, listed in column-I. Some effects which may occur in new steady state due to these changes on the capacitor 2 are listed in column-II. Match the changes one capacitor 1 in column-I with corresponding effect on capacitor 2 in column-II.

+ _

Cap.1

Cap.2

Column I (A) A dielectric slab is inserted. (B) Separation between plates increased. (C) A metal plate is inserted connecting both plates (D) The left plate is grounded.

Column II (p) Charge on the capacitor increases. (q) Charge on the capacitor decreases. (r) Energy stored in the capacitor increases. (s) No change is occured.

ANSWERS 1.

D

2.

A

3.

D

4.

C

5.

A

6.

C

7.

D

8.

C

9.

B

10.

A

11.

B

12.

C

13.

C

14.

A

15.

C

16.

A

17.

C

18.

B

19.

B

20.

ACD

21.

AC

22.

ABCD 23.

AC

24.

A

25.

C

26.

A

27.

D

28.

B

29.

B

D

31.

B

32.

13 0 A 10 d

33.

Req =

34.

(a) R = 0 , (b)

37.

(a) P (b) P (c) R (d) R 38.

30.

RESONANCE

R=

r 35. 2

2R R = 4 2

From (1) & (2) R = r

36.

(A) q (B) s (C) s (D) q

(A) s (B) p, s (C) p, r (D) q, r

39.

(A) p, r (B) q (C) p,r (D) s

8

REVISION TEST - 09 Course : VIJAY (R) TOPIC : EMF Time : 3 Hrs.

Max. Marks : 117

Instructions : 1. For each correct Single choice question 3 marks (with 1 mark negative marking). 2. For each correct Multiple choice question 3 marks (with 1 mark negative marking). 3. For each correct answer in Comprehension 4 marks (with 1 mark negative marking). 4. For each correct Assertion/Reason question 3 marks (with 1 mark negative marking). 5. For each correct Subjective question 6 marks (with no negative marking). 6. For each correct Match the column question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

An electron (charge e, mass ' m ' ) is revolving around a fixed proton in circular path of radius ' r '. The magnetic field at the centre due to electron is: (A) 0

0 e2

(B)

8r 2.

3.

2

m0 r

0 e

(C)

0 e

(D)

8 r m0 r

4r

2

m0 r

A point charge is moving in clockwise direction in a circle with constant speed. Consider the magnetic field produced by the charge at a point P (not centre of the circle) on the axis of the circle. (A) it is constant in magnitude only (B) it is constant in direction only (C) it is constant in direction and magnitude both (D) it is not constant in magnitude and direction both. A particle is moving with velocity v ˆi 3ˆj and it produces an electric field at a point given by E 2kˆ . It will produce magnetic field at that point equal to (all quantities are in S.. units) (A)

4.

6 ˆi 2ˆj c2

(B)

6ˆi 2ˆj c2

(C) zero

(D) can not be determined from the given data

Two observers moving with different velocities see that a point charge produces same magnetic field at the same point A . Their relative velocity must be parallel to r , where r is the position vector of point A with respect to point charge. This statement is : (A) true (B) false (C) nothing can be said (D) true only if the charge is moving perpendicular to the r

5.

A uniformly charged ring of radius R is rotated about its axis with constant linear speed v of each of its particles. The ratio of electric field to magnetic field at a point P on the axis of the ring distant x = R from centre of ring is (c is speed of light)

(A)

6.

c2 v

(B)

v2 c

(C)

c v

(D)

v c

(D)

2 0 d

If the magnetic field at 'P' can be written as K tan then K is : 2

[Refer to the figure of question no. 8] (A)

0 4d

RESONANCE

(B)

0 2d

(C)

0 d

1

7.

The magnetic field at the origin due to the current flowing in the wire is

(A)

0 ˆ ˆ (i k) 8 a

(B)

0 ˆ ˆ (i k) 2 a

(C)

0 ˆ ˆ ( i k) 8 a

(D)

0 4a 2

8.

A negative charge is given to a loop and the loop is rotated in the plane of paper about its centre as shown. The magnetic field produced by the ring affects a small magnet placed above the ring in the same plane of paper. (A) the magnet does not rotate (B) the magnet rotates clockwise as seen by observer from below (C) the magnet rotates anti-clockwise as seen from below (D) none of the above.

9.

A nonconducting disc having uniform positive charge Q, is rotating about its axis with uniform angular velocity . The magnetic field at the center of the disc is.

10.

(A) directed outward

0Q (B) having magnitude 4 R

(C) directed inwards

0Q (D) having magnitude 2 R

( ˆi kˆ )

A uniform circular loop of radius a and resistance R is pulled at a constant velocity v out of a region of uniform magnetic field whose magnitude is B. The plane of loop and the velocity are both perpendicular to B . Then the electrical power in the circular loop at the instant when the arc (of circular loop) outside the region of magnetic field subtends an angle at centre of the loop is : 3

B 2a 2 v 2 2B 2a 2 v 2 B 2a 2 v 2 (B) (C) (D) None of these R R 2R An electron moving with velocity V along the axis approaches a circular current carrying loop as shown in the figure. The magnitude of magnetic force on electron at this instant is

(A) 11.

(A)

0 e v iR 2 x 2 ( x 2 R 2 )3 / 2

RESONANCE

(B) 0

e v iR 2 x ( x 2 R 2 )3 / 2

(C)

0 e v iR 2 x 4 ( x 2 R 2 )3 / 2

(D) 0

2

12.

q is entering in a magnetic field of strength B at a m speed v = (2d)(B), then which of the following is correct : If a charged particle of charge to mass ratio

(A) (B)

(C) (D) 13.

14.

angle subtended by charged particle at the centre of circular path is 2. the charge will move on a circular path and will come out from magnetic field at a distance 4d from the point of insertion. 2 the time for which particle will be in the magnetic field is . B the charged particle will subtend an angle of 900 at the centre of circular path

A proton moves in the positive z-direction after being accelerated from rest through a potential difference V. The proton then passes through a region with a uniform electric field E in the positive x-direction and a uniform magnetic field B in the positive y-direction, but the proton's trajectory is not affected. If the experiment were repeated using a potential difference of 2V, the proton would then be (A) deflected in positive x-direction (B) deflected in negative x-direction (C) deflected in positive y-direction (D) deflected in negative y-direction In region x > 0, a uniform and constant magnetic field B1 2 B 0 kˆ exists. Another uniform and constant magnetic field B 2 B 0 kˆ exists in region x < 0. A positively charged particle of mass m and charge q is crossing origin at time t = 0 with a velocity u u 0 ˆi . The particle comes back to its initial position after a time : (B0, u0 are positive constants)

3 m (A) 2 q B 0

2m (B) qB 0

3m (C) qB 0

(D) Particle does not come back to its initial position. 15.

16.

Figure shows an equilateral triangle ABC of side carrying currents, placed in uniform magnetic field B. The magnitude of magnetic force on triangle is : (A) iB

(B) 2 iB

(C) 3iB

(D) zero

Two long wires which are perpendicular to each other carry currents as shown in the figure. They are free to move. Consider only magnetic interaction

(A) the two wires will come closer transitionally (B) the two wires will move away transitionally (C) the two wires will rotate such that the currents become uni-directional and then come closer due to attraction (D) the two wires will rotate such that the currents become anti-parallel and then move far away due to repulsion.

RESONANCE

3

17.

A uniform, constant magnetic field B is directed at an angle of 45° to the x-axis in the xy-plane, PQRS is a rigid square wire frame carrying a steady current 0, with its centre at the origin O. At time t = 0, the frame is at rest in the position shown in the figure, with its sides parallel to the x and y axes. Each side of the frame is of mass M and length L.

The torque about O acting on the frame due to the magnetic field will be

(A) =

B 0L2 2

2 B L ˆi ˆj i j (B) = 0

2

(C) =

B 0L2 2

ˆi ˆj (D) =

B 0L2 2

ˆi ˆj

MULTIPLE CHOICE QUESTIONS 18.

A single circular loop of wire with radius 0.02 m carries a current of 8.0 A. It is placed at the centre of a solenoid that has length 0.65 m, radius 0.080 m and 1300 turns. Solenoid

Current carrying loop

(A) The value of the current in the solenoid so that the magnetic field at the centre of the loop becomes zero, is equal to 44 mA. (B) The value of the current in the solenoid so that the magnetic field at the centre of the loop becomes zero, is equal to 100 mA. (C) The magnitude of the total magnetic field at the centre of the loop (due to both the loop and the solenoid) if the current in the loop is reversed in direction from that needed to make the total field equal to zero tesla, is 8 x 10–5 T. (D) The magnitude of the total magnetic field at the centre of the loop (due to both the loop and the solenoid) if the current in the loop is reversed in direction from that needed to make the total field equal to zero tesla, is 16 x 10–5 T. 19.

A particle of charge ‘q’ & mass ‘m’ enters normally (at point P) in a region of magnetic field with speed v. It comes out normally from Q after time T as shown in figure. The magnetic field B is present only in the region of radius R and is uniform. Initial and final velocities are along radial direction and they are perpendicular to each other. For this to happen, which of the following expression(s) is/are correct : (A) B =

mv qR

(B) T =

R 2v

(C) T =

m 2qB

(D) None of these

20.

Figure shows the path of an electron in a region of uniform magnetic field. The path consists of two straight sections, each between a pair of uniformly charged plates, and two half circles. The electric field exists only between the plates. (A) Plate I of pair A is at higher potential than plate-II of the same pair. (B) Plate I of pair B is at higher potential than plate II of the same pair. (C) Direction of the magnetic field is out of the page [ ]. (D) Direction of the magnetic field in to the page [ ].

RESONANCE

Pair-A

Pair-B

4

COMPREHENSION Comprehension

As a charged particle ‘q’ moving with a velocity v enters a uniform magnetic field B , it experiences a force F = q (v B ) . For = 0º or 180º, being the angle between v and B , force experienced is zero and the particle passes undeflected. For = 90º, the particle moves along a circular arc and the magnetic force mv 2 . For other values of ( 0º, 180º, 90º), the charged (qvB) provides the necessary centripetal force r particle moves along a helical path which is the resultant motion of simultaneous circular and translational motions. Suppose a particle, that carries a charge of magnitude q and has a mass 4 × 10–15 kg, is moving in a region containing a uniform magnetic field B = – 0.4 kˆ T. At some instant, velocity of the particle is v =

(8iˆ 6 ˆj 4kˆ) × 106 m/s and force acting on it has a magnitude 1.6 N. 21.

Motion of charged particle will be along a helical path with : (A) A translational component along x-direction and a circular component in the y-z plane (B) A translational component along y-direction and a circular component in the x-z plane (C) A translational component along z-axis and a circular component in the x-y plane (D) Direction of translational component and plane of circular component are uncertain

22.

Angular frequency of rotation of particle, also called the ‘cyclotron frequency’ is : (A) 8 × 105 rad/s (B) 12.5 × 104 rad/s (C) 6.2 × 106 rad/s (D) 4 × 107 rad/s

23.

If the coordinates of the particle at t = 0 are (2 m, 1 m, 0), coordinates at a time t = 3 T, where T is the time period of circular component of motion, will be (take = 3.14) : (A) (2 m, 1 m, 400 m) (B) (0.142 m, 130 m, 0) (C) (2 m, 1 m, 1.884 m) (D) (142 m, 130 m, 628 m)

ASSERTION / REASON 24.

Statement 1 : A direct uniformly distributed current flows through a solid long metallic cylinder along its length. It produces magnetic field only outside the cylinder . Statement 2 : A thin long cylindrical tube carrying uniformly distributed current along its length does not produce a magnetic field inside it. Moreover, a solid cylinder can be supposed to be made up of many thin cylindrical tubes. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

25.

STATEMENT-1 : A pendulum made of an insulated rigid massless rod of length is attached to a small sphere of mass m and charge q. The pendulum is undergoing oscillations of small amplitude having time period T. Now a uniform horizontal magnetic field B out of plane of page is switched on. As a result of this change, the time period of oscillations does not change.

STATEMENT-2 : A force acting along the string on the bob of a simple pendulum (such that tension in string is never zero) does not produce any restoring torque on the bob about the hinge. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

RESONANCE

5

26.

STATEMENT–1 : No electric current will be present within a region having uniform and constant magnetic field. STATEMENT–2 : W ithin a region of uniform and constant magnetic field B , the path integral of magnetic field B d along any closed path is zero. Hence from Ampere circuital law B d o I

(where the given terms have usual meaning), no current can be present within a region having uniform and constant magnetic field. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True.

SUBJECTIVE CHOICE QUESTIONS 27.

A thin beam of charged particles is incident normally on the boundary of a region containing a uniform magnetic field as shown. The beam comprise of monoenergetic and – particles, each possessing a kinetic energy T. Neglecting interaction between particles of the beam, find the separation between the and particles when they emerge out of the magnetic field. (express your answer in terms of T, B, e, me & m, where all terms have their usual meanings.) (Te T )

28.

The given fig. shows a coil bent with AB = BC = CD = DE = EF = FG = GH = HA = 1 m and carrying current 1 A. There exists in space a vertical uniform magnetic field of 2 T in the y-direction. Then find out the torque (in vector form) on the loop.

MATCH THE COLUMN 29.

A beam consisting of four types of ions A, B, C and D enters a region that contains a uniform magnetic field as shown. The field is perpendicular to the plane of the paper, but its precise direction is not given. All ions in the beam travel with the same speed. The table below gives the masses and charges of the ions. Region containing Magnetic field

1

2

3 r4

r2

r1 Ion beam

RESONANCE

4

r3

ION A B C D

MASS 2m 4m 2m m

CHARGE e –e –e +e

r4 > r3 = r2 > r1

6

The ions fall at different positions 1, 2, 3 and 4, as shown. Correctly match the ions with respective falling positions.

30.

Column

Column

(a) A

(P) 1

(b) B

(Q) 2

(c) C

(R) 3

(d) D

(S) 4

A charged particle having non zero velocity is subjected to certain conditions given in Column . Column gives possible trajectories of the particle. Match the conditions in column with the results in Coulmn Column

31.

Column

(A)

In only uniform electric field

(p) the path of the charged particle may be a straight line

(B)

In only uniform magnetic field

(q) the path of the charged particle may be a parabola

(C)

In uniform magnetic and uniform electric field such that both are parallel

(r) the path of the charged particle may be a circle

(D)

Subjected to a net force of constant magnitude

(s) the path of the charged particle may be a helix with uniform or non uniform pitch

A uniform and constant magnetic field exists in whole space as shown by magnetic lines of forces. Each of the four particles 1, 2, 3 and 4 have charge +q and mass m. Each of the particle is given a initial velocity of magnitude 'v '; the angle between initial velocity of each particle and magnetic field is shown (velocity of particle 2 is along the magnetic field and velocity of particle 4 is perpendicular to magnetic field). Neglect electrostatic and magnetic force on each charge due to remaining three charges. Match the statements in column-I with particle(s) they correspond to in column-II.

Column-I

Column-II

(A)

The magnitude of angle between velocity and magnetic field does not change for

(p) Particle 1

(B)

Total distance travelled in time 't' is equal to 'vt ' for

(q) Particle 2

(C)

The magnitude of acceleration is non zero and constant for

(r) Particle 3

(D)

If a uniform electric field is switched on in direction of existing magnetic field, the name of the path of trajectory becomes different for

(s) Particle 4

RESONANCE

7

32.

A square wire frame ABCD is made of four thin uniform rods of length 'a' each. The charge per unit length on each of four rods is uniform and . The frame moves in x-y plane (z = 0 plane) with constant velocity v v 0 ˆi , the centre of frame always lies on x-axis and side BC is parallel to y-axis. At the instant centre of frame is at origin, match the positions in column- with respective nature of fields in column-II.

Column-I

Column-II

(A) At point P whose coordinates are (4a, 0, 0)

(p) magnitude of magnetic field is zero

(B) At point Q whose coordinates are (0, 4a, 0)

(q) magnitude of magnetic field is nonzero

(C) At point R whose coordinates are (0, 0, 4a)

(r) magnitude of electrostatic field is zero

(D) At origin

(s) magnitude of electrostatic field is nonzero

ANSWERS 1.

B

2.

A

3.

A

4.

A

5.

A

6.

B

7.

C

8.

B

9.

AD

10.

A

11.

D

12.

B

13.

B

14.

B

15.

A

16.

C

17.

A

18.

BD

19.

ABC

20.

ABC

21.

C

22.

D

23.

C

24.

D

25.

A

26.

A

27.

2 2T m m e eB 2

28.

2 kˆ units

29.

(a) S (b) P (c) Q (d) R

30.

(A) p, q ; (B) p, r, s ; (C) p, s ; (D) p, q, r, s

31.

(A) p,q,r,s, (b) p,q,r,s, (c) p,r,s (d) s

32.

(A) p,s (B) q,s (C) q,s (D) p,r

RESONANCE

8

View more...
Max. Marks : 133

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative making). 2. For each correct multiple choice question 4 marks (no negative marking). 3. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 4. For each match the column question 6 marks (no negative marking). 5. For each correct assertion/reason question 3 marks (with 1 mark negative marking).

SINGLE CHOICE QUESTIONS 1.

A particle is projected from origin O with a velocity (30 i + 40 j) m/s. Then the position vector of the particle 5 seconds later is : (take g = 10 m/s2) (A) 150 i + 200j m (B) 150 i + 75 j m (C) 30i + 75j m (D) Nothing can be predicted.

2.

For a particle moving in a straight line, the displacement of the particle at time t is given by S = t3 – 6t2 + 3t + 7 What is the velocity of the particle when its acceleration is zero? (A) – 9 m s–1 (B) – 12 m s–1 (C) 3 m s–1 (D) 42 m s–1

3.

The velocity of a particle moving on the x-axis is given by v = x2 + x where v is in m/s and x is in m. Find its acceleration in m/s2 when passing through the point x = 2m (A) 0 (B) 5 (C) 11 (D) 30

4.

A parachutist drops freely from an aeroplane for 10 s before the parachute opens out. Then he descends with a net retardation of 2.5 ms–2. If he bails out of the plane at a height of 2495 m and g = 10 ms–2, his velocity on reaching the ground will be (A) 2.5 ms–1 (B) 7.5 ms–1 (C) 5 ms–1 (D) 10 ms–1

5.

A particle can travel from point A to B from two different paths 1 and 2, as shown, in same interval of time. Then which of the following is incorrect? (A) Average velocity along the two paths must be equal (B) The particle may travel along both the paths unaccelerated (C) The direction of instantaneous velocity along the path 1 & 2 can be same for a maximum of two point on the paths. (D) The average and instantaneous velocity along path 1 can have same direction.

6.

Two trains, which are moving along different tracks in opposite directions, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are 300 m apart. Graphs given below show their velocities as function of time as the trains slow down. The separation between the trains when both have stopped, is :

(A) 120 m

RESONANCE

(B) 280 m

(C) 60 m

(D) 20 m.

1

7.

Position (Km) - Time (min.) graph is shown for two cars ‘A’ and ‘B’. Both collide at time t = 150 minute. Then the distance of position ‘R’ of accident from the starting point ‘Q’ of car A will be. (Initial distance between the two cars is 500 km) (Position in the graph shows the distance of the two cars from the point ‘Q’) (A) 200 km (B) 300 km (C) 250 km (D) 400 km

8.

A particle starts from rest with uniform acceleration and its velocity after n seconds is v. The displacement of the body in last two seconds is (A)

v(n 1) n

(B)

2v(n 1) n

(C)

2v(n 1) n

(D)

v(n 1) n

9.

A boat is rowed across a river at the rate of 4.5 km/hr. The river flows at the rate of 6 km/hr. The velocity of boat in m/s is: (A) 3.1 (B) 2.1 (C) 2.9 (D) 5

10.

An aeroplane is to go along straight line from A to B, and back again. The relative speed with respect to wind is V.. The wind blows perpendicular to line AB with speed . The distance between A and B is l. The total time for the round trip is: 2

(A) 11.

2

V v

2

(B)

2v 2

V v

2

(C)

2

2V 2

V v

2

A man can swim in still water with a speed of 3 m/s. x and y axis are drawn along and normal to the bank of river flowing to right with a speed of 1 m/s. The man starts swimming from origin O at t = 0 second. Assume size of man to be negligible. Find the equation of locus of all the possible points where man can reach at t = 1 sec. (A) (x – 1)2 + y2 = 3 (B) (x – 1)2 + y2 = 9 2 2 (C) x + (y – 1) = 3 (D) x2 + (y – 1)2 = 9

(D)

V 2 v 2 y Vriver=1m/s

river

flow x

O

12.

P is a point moving with constant speed 10 m/s such that its velocity vector always maintains an angle 60° with line OP as shown in figure (O is a fixed point in space). The initial distance between O and P is 100 m. After what time shall P reach O. (A) 10 sec. (B) 15 sec. (C) 20 sec. (D) 20 3 sec

13.

During a rainy day, rain is falling vertically with a velocity 2m/s. A boy at rest starts his motion with a constant acceleration of 2m/s2 along a straight road. Find the rate at which the angle of the axis of umbrella with vertical should be changed so that the rain always falls parallel to the axis of the umbrella. (A)

1 1 t

2

(B)

2 1 t

2

(C)

1 2t

2

(D)

1 1 2t 2

14.

A train is standing on a platform , a man inside a compartment of a train drops a stone . At the same instant train starts to move with constant acceleration . The path of the particle as seen by the person who drops the stone is : (A) parabola (B) straight line for sometime & parabola for the remaining time (C) straight line (D) variable path that cannot be defined

15.

Two boats A and B having same speed relative to river are moving in a river. Boat A moves normal to the river current as observed by an observer moving with velocity of river current. Boat B moves normal to the river as observed by the observer on the ground. (A) To a ground observer boat B moves faster than A (B) To a ground observer boat A moves faster than B (C) To the given moving observer boat B moves faster than A (D) To the given moving observer boat A moves faster than B

RESONANCE

2

16.

For four particles A, B, C & D, the velocities of one with respect to other are given as V DC is 20 m/s towards north, V BC is 20 m/s towards east and V BA is 20 m/s towards south. Then V DA is (A) 20 m/s towards north (B) 20 m/s towards south (C) 20 m/s towards east (D) 20 m/s towards west

MULTIPLE CHOICE QUESTIONS 17.

A particle moves in xy plane in such a way that its distance ‘r’ from the origin depends upon time ‘t’ as r = 3t. The angle ‘’ made by its position vector with the positive x-axis at any time ‘t’ is given as ; = 2t. Here r is in metres, in rad and t in seconds. (A) The particle moves in circular motion. (B) At time t = 0.5 s, its speed is 3 2 m/s. (C) At time t = 0.5 s, its velocity vector makes an angle 45° with its position vector at the same time. (D) At time t = 0.5 s, its velocity vector makes an angle 30° with its position vector at the same time.

18.

Two particles, one with constant velocity 50m/s and the other with uniform acceleration 10m/s 2, start moving simultaneously from the same position in the same direction. They will be at a distance of 125m from each other after (A) 5 sec. (B) 5(1 + 2) sec. (C) 10sec. (D) 10(2 + 1)sec.

19.

A man standing on the edge of the terrace of a high rise building throws a stone vertically up with a speed of 20 m/s. Two seconds later an identical stone is thrown vertically downwards with the same speed of 20 m/s. Then: (A) the relative velocity between the two stones remain constant till one hits the ground (B) both will have the same kinetic energy when they hit the ground (C) the time interval between their hitting the ground is 2 seconds (D) if the collisions on the ground are perfectly elastic both will rise to the same height above the ground.

20.

A cart with a mass M = 1/2 kg is connected by a string to a weight of mass m = 200 g. At the initial moment the cart moves to the left along a horizontal plane at a speed V0 = 7 ms 1. All the surfaces are smooth (g = 9.8 ms 2) (A) the distance covered by cart in 5 s is zero (B) after 5 s weight of mass m will be in same position (C) the distance covered by cart in 5 s is 17.5 m (D) none of the above A particle moves with an initial velocity v 0 and retardation v, where v is its velocity at any time t ( is a positive constant). (A) the particle will cover a total distance of v 0/ (B) the particle will continue to move for a very long time (C) the particle will stop shortly (D) the velocity of particle will become v 0/2 after time 1/.

21.

22.

A particle is moving rectilinearly so that its acceleration is given as a = 3t2+1 m/s2.Its initial velocity is zero. (A) The velocity of the particle at t=1 sec will be 2m/s. (B) The displacement of the particle in 1 sec will be 2m. (C) The particle will continue to move in positive direction. (D) The particle will come back to its starting point after some time.

23.

A man is standing on a road and observes that rain is falling at angle 45º with the vertical. The man starts running on the road with constant acceleration 0.5 m/s 2. After a certain time from the start of the motion, it appears to him that rain is still falling at angle 45º with the vertical, with speed 2 2 m/s . Motion of the man is in the same vertical plane in which the rain is falling. Then which of the following statement(s) are true. (A) It is not possible (B) Speed of the rain relative to the ground is 2 m/s. (C) Speed of the man when he finds rain to be falling at angle 45º with the vertical, is 4m/s. (D) The man has travelled a distance 16m on the road by the time he again finds rain to be falling at angle 45°.

RESONANCE

3

COMPREHENSION Comprehension - 1 Raindrops are falling with a velocity 10 2 m/s making an angle of 450 with the vertical. The drops appear to be falling vertically to a man running with constant velocity. The velocity of rain drops change such that the rain drops now appear to be falling vertically with 3 times the velocity it appeared earlier to the same person running with same velocity. 24.

The magnitude of velocity of man with respect to ground is (A) 10 2 m/s

25.

(C) 20 m/s

(D) 10 m/s

After the velocity of rain drops change, the magnitude of velocity of raindrops with respect to ground is (A) 20 m/s

26.

(B) 10 3 m/s

(B) 20 3 m/s

(C) 10 m/s

(D) 10 3 m/s

The angle (in degrees) between the initial and the final velocity vectors of the raindrops with respect to the ground is (A) 8 (B) 15 (C) 22.5 (D) 37

Comprehension - 2 A overhead bridge, a subway and a road start from A and again meet at B. The minimum distance between A and B, which is same as the length of the road AB, is 2 km. The overbridge and the subway form a semicircular arc above and below the road. A laser sensor is fixed (embedded) in the road. An Autorickshaw takes the overbridge from A and a taxi takes the subways from B.The laser sensor gives a beep when the linear distances between point A and the autorickshaw is same as that between the rickshaw and the laser sensor which also equals the distance of laser source from point A. 27.

If the time t, for the laser starts when the autorickshaw just enters the bridge from point A and at t = 240 sec, laser the gives a beep, what is the speed of the autorickshaw ? (A) 4.36 m/s (B) 1.21 m/s (C) 8.16 m/s (D) 16.32 m/s

28.

The autorickshaw takes the overhead bridge from A and on reaching B, immediately takes the subway to come back to A, while the taxi starts from B travels to and fro from B to A continuously by road. If the auto and the taxi travel with constant speeds of

km/hr and 3 km/hr respectively, how frequently do 2

they meet at A ? (A) every 4 hours

(C) every 29.

(B) every

2 hours 3

2n hours, n = 3,6,9,.... 3

(D) they never meet

Due to heavy rains, the flyover and the roads were blocked and all the vehicles had to take the subway. The autorickshaw and the taxi started from A and B respectively with the speeds

2 and km/hr 3 2

respectively. After how much time did they meet ? (A)

7 hours 6

RESONANCE

(B)

6 hours 7

(C)

2 hours 3

(D)

6 hours 7

4

Comprehension - 3 Mr. Shyam drives his car at uniform speed from bottom of a mountain to the top in 20 minutes along a helical path as shown. At the beginning the speedometer of his car shows 8315 km, while on reaching the top it reads 8335 km.(Take upward as positive yaxis and positive x-axis towards right) 30.

31.

The total distance covered is : (A) 10 km (B) 20 km

(D) can not be determine

His displacement vector during the journey is : (A) ( 3 ˆi 4 ˆj ) km

32.

(C) 25 km

(B) 3 km

(C) 5 km

(D) none of these

(C) (25/8) m/s

(D) None of these

The average velocity during the journey is : (A) (9 ˆi 12ˆj) km/hr

(B) (2.5 ˆi 3.3 ˆj) m/s

MATCH THE COLUMN 33.

Two particles A and B moving in x-y plane are at origin at t = 0 sec. The initial velocity vectors of A and B are u A = 8 ˆi m/s and uB = 8 ˆj m/s. The acceleration of A and B are constant and are a A = –2 ˆi m/s 2 and a B = – 2 ˆj m/s 2. Column gives certain statements regarding particle A and B. Column gives corresponding results. Match the statements in column with corresponding results in Column . Column I Column II

34.

(A) The time (in seconds) at which velocity of A relative to B is zero

(p) 16 2

(B) The distance (in metres) between A and B when their relative velocity is zero. (C) The time (in seconds) after t = 0 sec, at which A and B are at same position (D) The magnitude of relative velocity of A and B at the instant they are at same position.

(q) 8 2 (r) 8 (s) 4

A particle is moving along a straight line. Its velocity varies with time as v = kt, where k is a positive constant and t is the time. Match the graphs in Column with the statements in Column Column Column

(A) Acceleration versus time curve

(p)

(B) Acceleration versus displacement curve

(q)

(C) Velocity versus time curve

(r)

(D) Displacement versus velocity curve

(s)

RESONANCE

5

ASSERTION / REASON 35.

Assertion : If acceleration of a particle is decreasing then it is possible that velocity is increasing with time. Reason : Acceleration is rate of change of velocity. (A) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. (B) If both Assertion and Reason are true, but Reason is not correct explanation of the Assertion. (C) if Assertion is true, but the Reason is false. (D) if Assertion is false, but the Reason is true.

36

STATEMENT–1 : The equation of distance travelled by a particle moving in a straight line with constant acceleration in nth second is Sn = u + (2n – 1)

a , where letters have usual meaning, is dimensionally 2

incorrect. STATEMENT–2: For every equation relating physical quantities to be true, it must have dimensional homogenity. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. 37.

STATEMENT-1 : The magnitude of velocity of two boats relative to river is same. Both boats start simultaneously from same point on one bank may reach opposite bank simultaneously moving along different paths. STATEMENT-2 : For boats to cross the river in same time. The component of their velocity relative to river in direction normal to flow should be same. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

Answer Key (Revision Test - 01) 1. 6. 11. 16. 21. 26. 31. 34.

(B) 2. (D) 7. (B) 12. (D) 17. (A)(B) 22. (B) 27. (A) 32. (A) p (B) p (C) q (D) r

(A) (B) (C) (B)(C) (A)(C) (A) (A)

3. 8. 13. 18. 23. 28. 33. 35.

(D) 4. (C) (C) 9. (B) (A) 14. (C) (A)(B) 19. (A)(B)(C)(D) (C)(D) 24. (D) (D) 29. (B) (A) s (B) p (C) r (D) q (A) 36 (D)

5. 10. 15. 20. 25. 30.

(B) (A) (B) (B) (C) (A) (B)

37.

(A)

Solution will be provided with next revision test.

RESONANCE

6

REVISION TEST - 02 COURSE : VIJAY (R) TOPIC : PROJECTILE MOTION SUBJECT : PHYSICS Time : 1½ Hrs.

Max. Marks : 48

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative making). 2. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 3. For each match the column question 6 marks (no negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking).

SINGLE CHOICE QUESTIONS 1.

A particle when projected in vertical plane moves along the fixed smooth surface with initial velocity 20 m/s at an angle of 60º, so that its normal reaction on the surface remains zero throughout the motion. Then the slope of the tangent to the surface at height 5 m from the point of projection A will be: (A) 30º

2.

(B) 45º

(D) tan1 2

A particle moves along the parabolic path y = ax2 in such a way that the y-component of the velocity remains constant, say c. The x and y coordinates are in meters. Then acceleration of the particle at x =1 m is (A) ac kˆ

3.

(C) tan1 2

(B) 2ac 2 ˆj

(C)

c2 ˆ i 4a 2

(D)

c ˆ i 2a

An object is thrown from a point ‘A’ horizontally from a tower and hits the ground 3s later at B. The line from ‘A’ to ‘B’ makes an angle of 30º with the horizontal. The initial velocity of the object is : (take g = 10 m/s2) (A) 15 3 m/s

(B) 15 m/s

(C) 10

(D) 25 / 3 m/s

3 m/s

4.

A particle is projected from a point P (2, 0, 0)m with a velocity 10 m/s making an angle 45º with the horizontal. The plane of projectile motion passes through a horizontal line PQ which makes an angle of 37º with positive x-axis, xy plane is horizontal. The coordinates of the point where the particle will strike the line PQ is: (Take g = 10 m/s 2) (A) (10, 6, 0)m (B) (8, 6, 0)m (C) (10, 8, 0)m (D) (6, 10, 0)m

5.

A car starts with constant acceleration a = 2m/s2 at t = 0. Two coins are released from the car at t = 3 & t = 4. Each coin takes 1 second to fall on ground. Then the distance between the two coins will be (Assume coin sticks to the ground) (A) 9 m (B) 7 m (C) 15 m (D) 2m

6.

Velocity of a stone projected, 2 second before it reaches the maximum height, makes angle 53° with the horizontal then the velocity at highest point will be (A) 20 m/s (B) 15 m/s (C) 25 m/s (D) 80/3 m/s Two guns are mounted (fixed) on two vertical cliffs that are very high from the ground as shown in figure. The muzzle velocity of the shell from G1 is u1 and that from G2 is u2. The guns aim exactly towards each other The ratio u1 : u2 such that the shells collide with each other in air is (Assume that there is no resistance of air)

7.

(A) 1 : 2 (C) will not collide for any ratio 8.

(B) 1 : 4 (D) will collide for any ratio

A stone is projected from level ground such that its horizontal and vertical components of initial velocity are ux = 10 m/s and uy = 20 m/s respectively. Then the angle between velocity vector of stone one second before and one second after it attains maximum height is : (A) 30° (B) 45° (C) 60° (D) 90°

COMPREHENSION Comprehension A stone is projected from level ground with speed u and at an angle with horizontal. Some how the acceleration due to gravity (g) becomes double (that is 2g) immediately after the stone reaches the maximum height and remains same thereafter. Assume direction of acceleration due to gravity always vertically downwards.

RESONANCE

1

9.

The total time of flight of particle is :

3 u sin (A) 2 g 10.

(B)

u sin g

1 1 2

(C)

2u sin g

(D)

u sin 1 2 g 2

The horizontal range of particle is

u 2 sin 2 1 u 2 sin 2 1 3 u2 sin 2 u2 1 (C) 2 (B) sin2 (D) 2g 2g 4 g g 2 2 The angle which the velocity vector of stone makes with horizontal just before hitting the ground is given by : (A) tan = 2 tan (B) tan = 2 cot (C) tan = 2 tan (D) tan = 2 cot (A)

11.

MATCH THE COLUMN 12.

Match the following. The projectile collides perpendicularly with the inclined plane. (Refer the figure) u

(a) Maximum height attained by the projectile from the ground

(P) zero

(b) Maximum height attained by the projectile from Inclined plane

(Q) g

(c) Acceleration of the projectile before

(R)

u 2 sin 2 2 g cos

(S)

u 2 sin 2 ( ) 2g

striking the inclined plane (d) Horizontal component of acceleration of the projectile.

13.

Assertion : For a projectile up the incline maximum angle of projection can be where is angle 4 2 made by incline with horizontal.

Reason : Maximum range up the incline is given by

u2 where is angle made by incline with g(1 sin )

horizontal.. (A) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. (B) If both Assertion and Reason are true, but Reason is not correct explanation of the Assertion. (C) if Assertion is true, but the Reason is false. (D) if Assertion is false, but the Reason is true. 14.

STATEMENT-1 : Two stones are simultaneously projected from level ground from same point with same speeds but different angles with horizontal. Both stones move in same vertical plane. Then the two stones may collide in mid air. STATEMENT-2 : For two stones projected simultaneously from same point with same speed at different angles with horizontal, their trajectories may intersect at some point. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

Answer Key (Revision Test - 02) 1. 8. 13.

(D) (D) (D)

2. 9. 14.

(C) (B) (D)

3. 10.

(A) (B)

4. 11.

(A) (C)

5. 12.

(A) (a) S

6. (B) 7. (b) R (c) Q (d) P

(D)

Solution will be provided with next revision test.

RESONANCE

2

REVISION TEST - 03 COURSE : VIJAY (R) TOPIC : NLM & Friction SUBJECT : PHYSICS Time : 3 Hrs.

Max. Marks : 104

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative making). 2. For each correct multiple choice question 3 marks (with 1 mark negative making). 3. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking). 5. For each correct subjective question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

Two blocks A & B with mass 4 kg and 6 kg respectively are connected by a stretched spring of negligible mass as in figure. When the two blocks are released simultaneously the initial acceleration of B is 1.5 m/s 2 westward. The acceleration of A is : (A) 1 m/s 2 westward (B) 2.25 m/s 2 eastward (C) 1 m/s 2 eastward (D) 2.75 m/s 2 westward

2.

System shown in figure is in equilibrium. The magnitude of change in tension in the string just before and just after, when one of the spring is cut. Mass of both the blocks is same and equal to m and spring constant of both springs is k. (Neglect any effect of rotation) (A)

3.

4.

mg 2

(B)

mg 4

(C)

3m g 4

(D)

3m g 2

In the figure a block ‘A’ of mass ‘m’ is attached at one end of a light spring and the other end of the spring is connected to another block ‘B’ of mass 2m through a light string. ‘A’ is held and B is in static equilibrium. Now A is released. The acceleration of A just after that instant is ‘a’. In the next case, B is held and A is in static equilibrium. Now when B is released, its acceleration immediately after the release is 'b'. The value of a/b is : (Pulley, string and the spring are massless) 1 (A) 0 (B) undefined (C) 2 (D) 2 In the figure, at the free end of the light string, a force F is applied to keep the suspended mass of 18 kg at rest. Then the force exerted by the ceiling on the system (assume that the string segments are vertical and the pulleys are light and smooth) is: (g= 10 m/s2) (A) 60 N (D) 240 N

(B) 120 N (E) 200 N

(C) 180 N

5.

Two massless rings slide on a smooth circular loop of the wire whose axis lies in a horizontal plane. A smooth massless inextensible string passes through the rings, which carries masses m1 & m2 at the two ends and mass m3 between the rings. If there is equilibrium when the line connnecting each ring with centre substends an angle 300 with vertical as shown in figure. Then the ratio of masses are (A) m1 = 2m2 = m3 (B) 2m1 = m2 = 2m3 (C) m1 = m2 = m3 (D) None of these

6.

Four identical metal butterflies are hanging from a light string of length 5 at equally 1 placed points as shown. The ends of the string are attached to a horizontal fixed support. The middle section of the string is horizontal. The relation between the 2 angle 1 and 2 is given by (A) sin1 = 2 sin2 (B) 2cos1 = sin2 (C) tan1 = 2 tan2 (D) 2 < 1 and no other conclusion can be derived.

RESONANCE

1

7.

A bob is hanging over a pulley inside a car through a string . The second end of the string is in the hand of a person standing in the car . The car is moving with constant acceleration 'a' directed horizontally as shown in figure . Other end of the string is pulled with constant acceleration ' a ' (relative to car) vertically. The tension in the string is equal to (A) m g2 a 2

8.

(B) m g2 a 2 – ma

(D) m(g + a)

A wedge of height 'h' is released from rest with a light particle P placed on it as shown. The wedge slides down an incline which makes an angle with the horizontal. All the surfaces are smooth, P will reach the surface of the incline in time 2h

(A)

9.

(C) m g2 a 2 + ma

2

gsin

(B)

2h g sin cos

(C)

2h g tan

2h

(D)

g cos 2

In the given arrangement, mass of the block is M and the surface on which the block is placed is smooth. Assuming all pulleys to be massless and frictionless, strings to be inelastic and light, R1, R2 and R3 to be light supporting rods, then acceleration of point ‘P’ will be (Ais fixed) : (A) 0

(B)

(C)

4F m

(D)

2F m

10.

In the arrangement shown in the figure mass of the block B and A are 2 m,, 8 m respectively. Surface between B and floor is smooth. The block B is connected to block C by means of a pulley. If the whole system is released then the minimum value of mass of the block C so that the block A remains stationary with respect to B is : (Co-efficient of friction between A and B is and pulley is ideal) 10m m 2m 10 m (A) (B) (C) (D) 1 1 1

11.

A plank is held at an angle to the horizontal (Fig.) on two fixed supports A and B. The plank can slide against the supports (without friction) because of its weight Mg. With what acceleration and in what direction, a man of mass m should move so that the plank does not move. m (A) g sin 1 down the incline M

M (B) g sin 1 down the incline m

m (C) g sin 1 up the incline M

M (D) g sin 1 up the incline m

12.

A block of mass 20 kg is acted upon by a force F = 30 N at an angle 53° with the F horizontal in downward direction as shown. The coefficient of friction between the 53° block and the horizontal surface is 0.2. The friction force acting on the block by the ground is (g = 10 m/s2) (A) 40.0 N (B) 30.0 N (C) 18.0 N (D) 44.8 N

13.

A particle is resting over a smooth horizontal floor. At t = 0, a horizontal force starts acting on it. Magnitude of the force increases with time according to law F = t, where is a positive constant and t is time. For the figure shown which of the following statements is/are correct? (A) Curve 1 shows acceleration against time (C) Curve 2 shows velocity against acceleration

RESONANCE

(B) Curve 2 shows velocity against time (D) none of these 2

14.

An insect of mass m, starts moving on a rough inclined surface from point A. As the surface is very sticky, the coefficient of friction between the insect and the incline is = 1. Assume that it can move in any

A =1

direction ; up the incline or down the incline then (A) The maximum possible acceleration of the insect can be 14 m/sec 2 (B) The maximum possible acceleration of the insect can be 2 m/sec 2 (C) The insect can move with a constant velocity

=37°

(D) The insect can not move with a constant velocity Comprehension A block of mass M is kept in elevator (lift) which starts moving upward with constant acceleration 'b' as shown in figure. Initially elevator at rest. The block is observed by two observers A and B for a time interval t = 0 to t = T. Observer B is at rest with respect to elevator and observer A is standing on the ground.

15.

The observer A finds that the work done by gravity on the block is -

1 1 1 1 Mg2T2 (B) – Mg2T2 (C) Mg bT2 (D) – Mg bT2 2 2 2 2 The observer A finds that work done by normal reaction acting on the block is (A)

16.

(A)

1 M(g + b)2T2 2

(B) –

1 M(g + b)2T2 2

(C)

1 M(g + b) bT2 2

(D) –

1 M(g + b) bT2 2

17.

According to observer B (A) The work done by gravity on the block is zero (B) The work done by normal reaction on the block is zero (C) The work done by pseudo force on the block is zero (D) All the above are correct Q.18 to 23 (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 and Statement-2 both are False. (E) Statement-1 is False, Statement-2 is True. 18. Assertion (A) : If a body is not in rest position then the net external force acting on it cannot be zero. Reason (R) : If a body is moving with uniform speed it will continue doing so unless frictional force exceeds the force of motion. 19.

Assertion (A) : Two bodies of mass 50g and 20g are allowed to fall from the same height. If air resistance for each is same, then both the bodies reach the earth simultaneously. Reason (R) : Acceleration of both the bodies is same.

20.

Assertion (A) : Air is thrown on a sail attached to a boat from an electric fan placed on the boat, because of which some movement is caused in the boat. Reason (R) : When the fan pushes the sail by the air, then air also pushes the fan in the opposite direction, causing motion.

21.

Assertion (A) : A bird sitting on the floor of a wire cage and cage is in the hand of a boy. Even when the bird starts flying in the cage, the boy does not experience any change in the weight of the cage. Reason (R) : Bird is still in the cage because of which the boy does not experience any change.

RESONANCE

3

22.

Assertion (A) : A soda water bottle is falling freely the bubbles of the gas will not rise in water. Reason (R) : Pressure in the water does not increase with depth.

23.

Assertion (A) : When a ball is thrown upwards, its momentum first decreases and then increases. Reason (R) : Law of conservation of momentum is not followed is this process.

24.

Figure shows a moving truck, in which there is a bob 'A' and a block 'B' attached to a spring kept on the rough floor of truck. With respect to truck, (g = 10 m/sec 2) (Assume spring is massless) (a)

If bob A is in equilibrium at = 30º, the spring is in its natural state and the block B (mass =

3 kg) is also in equilibrium , find the minimum value of the coefficient of static friction between the block and the floor of truck. If now the acceleration of truck is changed so that the new angular position of A for which it is again in equilibrium is 45º, find the minimum elongation in spring when block B is in equilibrium assuming the value of the coefficient of static friction as that calculated in part (a).

(b)

25.

Collar A starts from rest & moves to the left with a constant acceleration. Knowing that after 30 s, the relative velocity of collar B w.r.t. collar A is 900 mm/s, determine the accelerations of A and B.

26.

In the arrangement shown in Figure mass of blocks A, B and C is 18.5 kg, 8 kg and 1.5 kg respectively. All the surfaces are smooth. System is released from rest at t = 0 & pulleys are light & frictionless. Calculate acceleration of block C.

27.

Figure shows an ideal pulley block of mass m = 1 kg, resting on a rough ground with friction coefficient µ = 1.5. Another block of mass M = 11 kg is hanging as shown. When system is released it is found that the magnitude of acceleration of point P on string is a. Find value of 4a in m/s2. (Use g = 10 m/s2)

28.

In which of the following cases the magnitude of acceleration of the block A will be maximum (Neglection friction, mass of pulley and string)

(i)

(ii)

m A

(iii)

m A

2m

m smooth

m

A

A

(iv)

2mg 2mg

B 2m

Answer Key (Revision Test - 03) 1. 7. 13. 19.

B C A,B,C D

2. 8. 14. 20.

24.

(a)

26. 27.

(i) 10 ms2 13

28.

(i) a =

A A A,C D

1 (b)

3

3. 9. 15. 21.

C C D D

3 1

4. 10. 16. 22.

D D C A

5. 11. 17. 23.

25.

10mm/s2

C B D A

6. 12. 18.

C C D

(ii) 0. 19 joule

2mg mg g = 3m 3

(ii) a =

2mg mg =g m

(iii) a =

2mg = 2g m

(iv) a =

2g 3

Solution will be provided with next revision test.

RESONANCE

4

REVISION TEST - 04 SUBJECT : PHYSICS Course : VIJAY (R) TOPIC : WPE & Circular Motion Time : 3 Hrs.

Max. Marks : 158

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative marking). 2. For each correct multiple choice question 4 marks (with 1 mark negative marking). 3. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 4. For each correct answer in match the column 6 marks (with no negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking). 5. For each correct subjective question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

2.

Select the correct alternative. (A) Work done by kinetic friction on a body always results in a loss of its kinetic energy. (B) Work done on a body, in the motion of that body over a close loop is zero for every force in nature. (C) Total mechanical energy of a system is always conserved no matter what type of internal and external forces on the body are present. (D) When total work done by a conservative force on the system is positive then the potential energy associated with this force decreases. A body of mass 1 kg is shifted from A to D on inclined planes by applying a force slowly such that the block is always is in contact with the plane surfaces. Neglecting the jerk experienced at points C and B, total work done by the force is :

(A) 90 J

(B) 56 J

(C) 180 J

(D) 0 J

3.

The cart starting from rest moves down the incline. When the cart maximally compresses the spring (that is compression in the spring is maximum) at the bottom of the track, the cart’s (A) velocity and acceleration are zero. (B) velocity is nonzero but its acceleration is zero. (C) acceleration is nonzero, but its velocity is zero. (D) velocity and acceleration are both nonzero.

4.

A horse drinks water from a cubical container of side 1 m. The level of the stomach of horse is at 2 m from the ground. Assume that all the water drunk by the horse is at a level of 2 m from the ground. Then minimum work done by the horse in drinking the entire water of the container is (Take water = 1000 kg/m3 and g = 10 m/s2 ) : (A) 10 kJ

RESONANCE

(B) 15 kJ

(C) 20 kJ

(D) zero

1

5.

A man places a chain (of mass ‘m’ and length ‘ ’) on a table slowly. Initially the lower end of the chain just touches the table. The man drops the chain when half of the chain is in vertical position. Then work done by the man in this process is : (A) – mg

2

(B) –

mg 4

(C) –

3mg 8

(D) –

mg 8

6.

In the track shown in figure section AB is a quadrant of a circle of 1 metre radius. A block is released at A and slides without friction until it reaches B. After B it moves on a rough horizontal floor and comes to rest at distance 3 metres from B. What is the coefficient of friction between floor and body ? (A) 1/3 (B) 2/3 (C) 1/4 (D) 3/8

7.

A particle of mass m moving along a straight line experiences force F which varies with the distance travelled as shown in the figure. If the velocity of the particle at x 0 is

(A) 2

2 F0 x 0 m

2 F0 x 0 , then velocity at 4 x 0 is: m

(B) 2

F0 x 0 m

(C)

F0 x 0 m

(D) none of these

8.

A block of mass m starts at rest at height h on a frictionless inclined plane. The block slides down the plane, travels across a rough horizontal surface with coefficient of kinetic friction , and compresses a spring with force constant k a distance x before momentarily coming to rest. Then the spring extends and the block travels back across the rough surface, sliding up the plane. The block travels a total distance d on rough horizontal surface. The correct expression for the maximum height h’ that the block reaches on its return is: (A) mgh’ = mgh – mgd (B) mgh’ = mgh + mgd (C) mgh’ = mgh + mgd + kx2 (D) mgh’ = mgh – mgd – kx2

9.

The figure shows a hollow cube of side 'a' of volume V. There is a small chamber of volume

V in the cube as 4 shown. This chamber is completely filled by m kg of water. Water leaks through a hole H and spreads in the whole cube. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is :

3 5 1 1 mg a (B) mg a (C) mga (D) mga 8 8 8 2 A particle is moving in a circular path. The acceleration and momentum vectors at an instant of time are ˆ a = 2 ˆi + 3 j m/s2 and P = 6 ˆi – 4 ˆj kgm/s. Then the motion of the particle is

(A) 10.

(A) uniform circular motion (C) circular motion with tangential retardation

RESONANCE

(B) circular motion with tangential acceleration (D) we cannot say anything from a and P given here.

2

11.

A bead of mass m is located on a parabolic wire with its axis vertical and vertex at the origin as shown in figure and whose equation is x2 = 4ay. The wire frame is fixed and the bead can slide on it without friction. The bead is released from the point y = 4a on the wire frame from rest. The tangential acceleration of the bead when it reaches the position given by y = a is :

(A) 12.

g 2

(B)

g

3g 2

(C)

g (D)

2

5

TTwo particles tied to different strings are whirled in a horizontal circle as shown in figure. The ratio of lengths of the strings so that they complete their circular path with equal time period is:

(A)

3 2

(B)

2 3

(C) 1

(D) None of these

13.

A smooth and vertical cone-shaped funnel is rotated with an angular velocity in such a way that an object on the inner wall of the funnel is at rest w.r.t. the funnel. If the object is slightly displaced along the slope from this position and released : (A) it will be in equilibrium at its new position. (B) it will execute SHM (C) it will oscillate but the motion is not SHM (D) none of these

14.

A ring of radius R lies in vertical plane. A bead of mass ‘m’ can move along the ring without friction. Initially the bead is at rest at the bottom most point on ring. The minimum constant horizontal speed v with which the ring must be pulled such that the bead completes the vertical circle (A)

15.

3gR

(C)

4gR

(D)

5gR

5 . 5 gR

A simple pendulum is oscillating in a vertical plane. If resultant acceleration of bob of mass m at a point A is in horizontal direction, find the tangential force at this point in terms of tension T and mg. (A) mg

16.

(B)

(B)

mg T

T 2 (mg)2

(C)

mg T

(mg)2 T 2

T (D) mg

(mg)2 T 2

The member OA rotates about a horizontal axis through O with a constant counter clockwise velocity = 3 rad/sec. As it passes the position = 0, a small mass m is placed upon it at a radial distance r = 0.5 m. If the mass is observed to slip at = 37º, the coefficient of friction between the mass & the member is ______.

(A)

3 16

RESONANCE

(B)

9 16

(C)

4 9

(D)

5 9

3

17.

A bob is attached to one end of a string other end of which is fixed at peg A. The bob is taken to a position where string makes an angle of 300 with the horizontal. On the circular path of the bob in vertical plane there is a peg ‘B’ at a symmetrical position with respect to the position of release as shown in the figure. If Vc and Va be the minimum speeds in clockwise and anticlockwise directions respectively, given to the bob in order to hit the peg ‘B’ then ratio Vc : Va is equal to : (A) 1 : 1

18.

(B) 1 :

(D) 1 : 4

A disc of radius R has a light pole fixed perpendicular to the disc at the circumference which in turn has a pendulum of length R attached to its other end as shown in figure. The disc is rotated with a constant angular velocity . The string is making an angle 300 with the rod. Then the angular velocity of disc is: 1/ 2

3 g (A) R 19.

(C) 1 : 2

2

1/ 2

g (C) 3R

3 g (B) 2R

1/ 2

2g (D) 3 3R

1/ 2

An automobile enters a turn of radius R. If the road is banked at an angle of 450 and the coefficient of friction is 1, the minimum and maximum speed with which the automobile can negotiate the turn without skidding is :

rg rg rg and rg (B) and rg (C) and 2 rg (D) 0 and infinite 2 2 2 A particle is projected horizontally from the top of a tower with a velocity v0. If v be its velocity at any instant, then the radius of curvature of the path of the particle at the point (where the particle is at that instant) is directly proportional to : (A) v3 (B) v2 (C) v (D) 1/v (A)

20.

MULTIPLE CHOICE QUESTIONS 21.

A double conical pendulum consists of two masses, m and M, connected by a massless string passing over a frictionless, massless pulley. The entire apparatus rotates freely at constant angular speed (rad/s) about the vertical axis (dashed line) passing through centre of pulley as shown. After the system comes in steady state, the length of string on either sides of pulley are small and L. Pick up the correct option(s).

(A)

cos m cos M

(B) cos =

g 2L

(C) m = ML

(D) cos =

g 2

22.

One of the forces acting on a particle is conservative then which of the following statement(s) are true about this conservative force (A) Its work is zero when the particle moves exactly once around any closed path. (B) Its work equals the change in the kinetic energy of the particle (C) Then that particular force must be constant. (D) Its work depends on the end points of the motion, not on the path between.

23.

In the figure, a block rests on the top of a smooth fixed hemispherical tube of radius R in which it can just fit. Two springs are connected to the base as shown. The block is given a small jerk so that it can slide on the hemisphere. The F-X (F is magnitude of force and x is compression) graph for the springs is given below. Which of the following may be possible : (A) The block will compress both springs by same amount. (B) The block will compress the springs during its to and fro motion about its original position by different amounts. (C) The block will perform to and fro motion along the hemispherical surface about the original position. (D) The block can never come to the original position.

RESONANCE

4

Comprehension One end of massless inextensible string of length is fixed and other end is tied to a small ball of mass m. The ball is performing a circular motion in vertical plane. At the lowest position, speed of ball is

24.

25. 26.

20 g .

Neglect any other forces on the ball except tension force and gravitational force. Acceleration due to gravity is g. Motion of ball is in nature of (A) circular motion with constant speed (B) circular motion with variable speed (C) circular motion with constant angular acceleration about centre of the circle. (D) none of these At the highest position of ball, tangential acceleration of ball is (A) 0 (B) g (C) 5 g (D) 16 g During circular motion, minimum value of tension in the string (A) zero (B) mg (C) 10 mg

(D) 15 mg

Comprehension : A body of mass m is moving along x-axis under the influence of conservative force with a potential energy given by

U(x) =

cx 2

x a2 Where c and a are positive constants. When displaced slightly from stable equilibrium position x = x0, it will experience restoring force proportional to its displacement, the force constant being d 2U 2 dx x x 0

27. 28. 29.

30.

The magnitude of force is maximum at : (A) x = 0 (B) x = + a

(C) x = – a

(D) no value of x

The body is in stable equilibrium at (A) x = 0 (B) x = +a

(C) x = – a

(D) both x = ± a

If body is at x = x0 where (i) x0 = 2a (ii) x0 = +a (iii) x0 = – a. If it is displaced slightly towards right, it will experience restoring force in (A) all the three cases (B) case (ii) only (C) case (iii) only (D) cases (i) and (ii) only. Match the statements in Column with the results in Column and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the OMR. (a) (b)

Column – I Work done by ideal gas during free expansion A wedge block system is as shown in the fig. The wedge lying on horizontal surface is accelerated to right by a horizontal force F. All surfaces are smooth. Work done by normal reaction exerted by wedge on block in any

Column – II (P) (Q)

zero non zero

time interval is (c)

(d)

Two identical conducting spheres of radius 'a' are separated (R) negative by a distance 'b' (b>>a). Both spheres carry equal and opposite charge. Net electrostatic potential energy of system of both spheres is A uniform cylinder lies over a rough horizontal platform. The (S) positive platform is accelerated horizontally as shown with acceleration a. The cylinder does not slip over the platform.The work done by the force of friction on the cylinder w.r.t ground in any time interval is

RESONANCE

5

31.

A particle is moving with speed v = 2t2 on the circumference of circle of radius R. Match the quantities given in column-I with corresponding results in column-II Column-I

Column-II

(A) Magnitude of tangential acceleration of particle (B) Magnitude of Centripetal acceleration of particle (C) Magnitude of angular speed of particle with respect to centre of circle (D) Angle between the total acceleration vector and centripetal acceleration vector of particle 32.

33.

(p) decreases with time. (q) increases with time (r) remains constant (s) depends on the value of radius R

In column-I condition on velocity, force and acceleration of a particle is given. Resultant motion is described in column-II. u = initial velocity, F = resultant force and v = instantaneous velocity.. Column-I Column-II (A) u F 0 and F = constant (p) path will be circular path (B) u F 0 and F = constant (q) speed will increase (C) v F 0 all the time and | F | = constant (r) path will be straight line and the particle always remains in one plane. (D) u 2 ˆi 3 ˆj and acceleration at all time a 6 ˆi 9 ˆj (s) path will be parabolic Each situation in column I gives graph of a particle moving in circular path. The variables , and t represent angular speed (at any time t) , angular displacement (in time t) and time respectively. Column gives certain resulting interpretation. Match the graphs in column with statements in column and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the OMR.

(A)

(p) Angular acceleration of particle is uniform

2

(B)

(q) Angular acceleration of particle is non-uniform 2

- graph

(C)

(r) Angular acceleration of particle is directly proportional to t. t - t graph

(D) t

2

(s) Angular acceleration of particle is directly proportional to .

2

- t graph

RESONANCE

6

34.

Net force on a system of particles in ground frame is zero. In each situation of column-I a statement is given regarding this system. Match the statements in column-I with the results in column-II. Column-I Column-II (A) Acceleration of centre of mass of system (p) is constant from ground frame (B) Net momentum of system from ground frame. (q) is zero (C) Net momentum of system from frame of centre (r) may be zero of mass of system (D) K.E. of system from frame of centre of mass (s) may be constant of system

35.

STATEMENT-1 : The sum of potential and kinetic energy for a system of moving objects is conserved only when no net external force acts on the objects STATEMENT-2 : If no nonconservative force acts on a system of objects, the work done by external forces on a system of objects is equal to change in potential energy plus change in kinetic energy of the system. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

36.

STATEMENT-1 : One end of ideal massless spring is connected to fixed vertical wall and other end to a block of mass m initially at rest on smooth horizontal surface. The spring is initially in natural length. Now a horizontal force F acts on block as shown. Then the maximum extension in spring is equal to maximum compression in spring. STATEMENT-2 : To compress and to expand an ideal unstretched spring by equal amount, same work is to be done on spring.

37.

STATEMENT-1 : For a particle moving in a circular path, if direction of angular velocity and angular acceleration is same, then angle between its velocity vector and acceleration vector increases. STATEMENT-2 : For a particle moving in a circular path with speed increasing at constant rate, the centripetal acceleration keeps on increasing (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True.

38.

STATEMENT-1 : A cyclist is cycling on a rough horizontal circular track with increasing speed. Then the net frictional force on cycle is always directed towards centre of the circular track. STATEMENT-2 : For a particle moving in a circle, component of its acceleration towards centre, that is, centripetal acceleration should exist (except when speed is zero instantaneously). (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

SUBJECTIVE QUESTIONS 39.

A ring of mass m can slide over a smooth vertical rod. The ring is connected to a spring of force constant K =

4 mg where 2 R is the natural length of the R

spring. The other end of the spring is fixed to the ground at a horizontal distance 2 R from the base of the rod. The mass is released at a height of 1.5 R from ground. (a) calculate the work done by the spring. (b) calculate the velocity of the ring as it reaches the ground.

RESONANCE

7

40.

A particle is being acted upon by one dimensional conservative force. In the F–x curve shown, four points A, B, C, D are marked on the curve. (a) State which type of equilibrium is the particle in at these positions. (b) Is the particle in equilibrium at all these points?

41.

A particle of mass 2kg starts to move at position x = 0 and time t = 0 under the action of force F= (10 + 4x) N along the x-axis on a frictionless horizontal track. Find the power delivered by the force in watts at the instant the particle has moved by the distance 5m.

42.

A rod AB is moving on a fixed circle of radius R with constant velocity ‘v’ as shown in figure. P is the point of 3R from centre of the circle. 5 The velocity of the rod is perpendicular to the rod and the rod is always parallel to the diameter CD.

intersection of the rod and the circle. At an instant the rod is at a distance x =

(a) Find the speed of point of intersection P. (b) Find the angular speed of point of intersection P with respect to centre of the circle. 43.

The block of mass m initially at x = 0 is acted upon by a horizontal force F = a bx2(where a > mg), as shown in the figure. The co-efficient of friction between the surfaces of contact is . The net work done on the block is zero, if the block travels a distance of ______.

1. 8. 15. 22. 29. 30. 32. 34.

D 2. A 3. C A 9. C 10. D B 16. A 17. C A,D 23. B,C 24. B D (A) p (B) q,s (C) q,s (D) q,s (A) r (B) q,s (C) p (D) q,r (A) p,q (B) p,r (C) p,q (D) r,s

Answer Key (Revision Test - 04)

39. 40.

41.

4. 11. 18. 25.

B C D A

5. 12. 19. 26.

C B D D

6. 13. 20. 27.

A D A A

31. 33. 35.

(A) q (B) q, s (C) q, s (D) p, s (A) q,s (B) p (C) p (D) q,r D 36. D 37. D

7. D 14. B 21.A,B,C,D 28. B

38.

D

mg R , 2 gR 2

(a)

Point

(b)

A No equilibrium B Unstable equilibrium C Stable equilibrium D Neutral equilibrium No, point A, F 0 i.e. particle is not in equilibrium

300

42.

(a)VP =

5 V 4

(b)

=

VP 5V = R 4R

43.

x = [3(a – mg)/b]½

Solution will be provided with next revision test.

RESONANCE

8

REVISION TEST - 05 Course : VIJAY (R) TOPIC : CENTER OF MASS Time : 3 Hrs.

Max. Marks : 129

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative marking). 2. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 3. For each correct answer in match the column 6 marks (with no negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking). 5. For each correct subjective question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

From the circular disc of radius 4 R two small disc of radius R are cut off. The centre of mass of the new structure will be : (Centre of lower circular cavity lies on x-axis and centre of upper circular cavity lies on y-axis) R R (A) ˆi ˆj 5 5

2.

(B) ˆi

R ˆR j 5 5

(C) ˆi

R ˆR j 5 5

(D)

3R ˆ ˆ ( i j) 14

The centre of mass of a non uniform rod of length L whose mass per unit length varies as k.x 2 where k is a constant & x is the distance of any point on rod from its one end, is (from the same end) L k 3 1 3k (A) L (B) L (C) (D) L 4 4 L Two semicircular rings of linear mass densities and 2 and of radius ‘R’ each are joined to form a complete ring. The distance of the center of the mass of complete ring from its centre is :

=

3.

3R 2R 3R (B) (C) (D) none of these 8 3 4 Both the blocks shown in the given arrangement are given together a horizontal velocity towards right. If acm be the subsequent acceleration of the centre of mass of the system of blocks, then acm equals (before sliding stops at all surfaces) (A) 0 m/s2 (B) 5/3 m/s2 (C) 7/3 m/s2 (D) 2 m/s2

(A) 4.

5.

6.

Two men ‘A’ and ‘B’ are standing on a plank. ‘B’ is at the middle of the plank and ‘A’ is the left end of the plank. System is initially at rest and masses are as shown in figure. ‘A’ and ‘B’ starts moving such that the position of ‘B’ remains fixed with respect to ground then‘A’ meets ‘B’. Then the point where A meets B is located at : (A) the middle of the plank (B) 30 cm from the left end of the plank (C) the right end of the plank (D) None of these Two balls of same mass are released simultaneously from heights h & 2h from the ground level. The balls collides with the floor & sticks to it. Then the velocity-time graph of centre of mass of the two balls is best represented by :

(A) 7.

8.

(B)

(C)

(D)

A cannon shell moving along a straight line bursts into two parts. Just after the burst one part moves with momentum 40 Ns making an angle 30º with the original line of motion. The minimum momentum of the other part of shell just after the burst is : (A) 0 Ns (B) 10 Ns (C) 20 Ns (D) 17.32 Ns Particle 'A' moves with speed 10 m/s in a frictionless circular fixed horizontal pipe of radius 5 m and strikes with 'B' of double mass that of A. Coefficient of restitution is 1/2 and particle 'A' starts its journey at t = 0. The time at which second collision occurs is : (A)

s 2

RESONANCE

(B)

2 s 3

(C)

5 s 2

(D) 4 s 1

9.

Three identical balls of mass m and radius R are placed on frictionless horizontal x-y plane. Ball A at (0, 0), Ball B at (4R, – 2 R) and ball C at (8R, – 2 2 R). Ball A is suddenly given an impulse P 2 mV ˆi . If collision between balls A and B is perfectly elastic while between B and C is perfectly inelastic, then the relative velocity of ball A with respect to ball C after a long time will be:

V ˆ V ˆ V ˆ V ˆ V ˆ 3V ˆ V ˆ 3V ˆ i i i i j j j j (B) (C) (D) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 A particle of mass m is moving along the x-axis with speed v when it collides with a particle of mass 2m initially at rest. After the collision, the first particle has come to rest, and the second particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the two pieces ? ( > 0) (A) Each piece moves with speed v. (B) Each piece moves with speed v/2. (C) One of the pieces moves with speed v/2, the other moves with speed greater than v/2 (D) Each piece moves with speed greater than v/2. (A)

10.

11.

A trolley filled with sand is moving with a velocity v on a smooth horizontal surface due to inertia. If the sand falls off at the rate of kg/sec, the velocity of the trolley as a function of time will be best represented by :

(A)

12.

(C)

(D)

In the fig. shown a cart moves on a smooth horizontal surface due to an external constant force of magnitude F. The initial mass of the cart is M0 and velocity is zero. Sand falls on to the cart with negligible velocity at constant rate kg/s and sticks to the cart. The velocity of the cart at time t is : (A)

13.

(B)

Ft M0 t

(B)

F t t e M0

(C)

Ft M0

(D)

Ft e t M0 t

In the figure, the block B of mass m starts from rest at the top of a wedge W of mass M. All surfaces are without friction. W can slide on the ground. B slides down onto the ground, moves along it with a speed v, has an elastic collision with the wall, and climbs back onto W. (A) B will reach the top of W again. (B) From the beginning, till the collision with the wall, the centre of mass of ‘B plus W’ is stationary. (C) After the collision, centre of mass of ‘B plus W’ moves with the horizontal component of velocity (D) When B reaches its highest position on W, the speed of W is

2mv m M

2mv . m M

Comprehension Figure shows block A of mass 0.2 kg sliding to the right over a frictionless elevated surface at a speed of 10 m/s. The block undergoes a collision with stationary block B, which is connected to a nondeformed spring of spring constant 1000 Nm–1. The coefficient of restitution between the blocks is 0.5. After the collision, block B oscillates in SHM with a period of 0.2 s, and block A slides off the left end of the elevated surface, landing a distance 'd' from the base of that surface after falling height 5m. (use 2 = 10; g = 10 m/s2) Assume that the spring does not affect the collision. 14. Mass of the block B is (A) 0.4 kg (B) 0.8 kg (C) 1 kg (D) 1.2 kg 15.

Amplitude of the SHM as being executed by block B-spring system, is

16.

(A) 2.5 10 cm (B) 10 cm The distance 'd' will be equal to (A) 2m (B) 2.5 m

RESONANCE

(C) 3 10 cm

(D) 5 10 cm

(C) 4m

(D) 6.25 m 2

Comprehension Figure shows an irregular wedge of mass m placed on a smooth horizontal surface. Part BC is rough.The other part of the wedge is smooth. 17.

What minimum velocity should be imparted to a small block of same mass m so that it may reach point B: (A) 2 gH

18.

(B)

2gH

(C) 2 g(H h)

(D) gh

The velocity of wedge when the block comes to rest (w.r.t. wedge) on part BC is :

(A) gH (B) g(H h (C) 2 gH (D) none of these If the coefficient of friction between the block and wedge is , and the block comes to rest with respect to wedge at a point D on the rough surface then BD will be H Hh h (A) (B) (C) (D) none of these Comprehension : A smooth rope of mass m and length L lies in a heap on a smooth horizontal floor, with one end attached to a block of mass M. The block is given a sudden kick and instantaneously acquires a horizontal velocity of magnitude V0 as shown in figure 1. As the block moves to right pulling the rope from heap, the rope being smooth, the heap remains at rest. At the instant block is at a distance x from point P as shown in figure-2 (P is a point on the rope which has just started to move at the given instant) , choose correct options for next three question. 20. The speed of block of mass M is 19.

mV0

(A) (M m x ) 21.

L

(C)

m3 L

V02 m (M x )3 L

(B)

V02 m (M x )3 L

mM 2 L

m 2 V0 m M (M x ) L

m4

(D)

V2

M2 V0 m m (M x ) L M2

0 (C) ML m (M x )3

V2

0 (D) L m (M x )3

L

L

The tension in rope at point P is (A)

23.

MV0 m (M x ) L

The magnitude of acceleration of block of mass M is (A)

22.

(B)

mM 2 L

V02 m (M x ) 2 L

(B)

m 2M L

V02 m (M x )2 L

(C)

m3 L

V02 m (M x ) 2 L

(D)

M3 L

V02 m (M x )2 L

In each situation of column-I a mass distribution is given and information regarding x and y-coordinate of centre of mass is given in column-II. Match the figures in column-I with corresponding information of centre of mass in column-II. Column-I Column-II (A) An equilateral triangular wire (p) xcm > 0 frame is made using three thin uniform rods of mass per unit lengths , 2 and 3 as shown (B) A square frame is made using four thin uniform rods of mass per unit length lengths , 2, 3 and 4 as shown

(q) ycm > 0

(C) A circular wire frame is made of two uniform semicircular wires of same radius and of mass per unit length and 2 as shown

(r)

(D) A circular wire frame is made of four uniform quarter circular wires of same radius and mass per unit length , 2, 3 and 4 as shown

(s) ycm < 0

RESONANCE

xcm < 0

3

25.

26.

27.

28. 29.

30.

31.

Two identical uniform solid spheres of mass m each approach each other with constant velocities such that net momentum of system of both spheres is zero. The speed of each sphere before collision is u. Both the spheres then collide. The condition of collision is given for each situation of column-I. In each situation of column- information regarding speed of sphere(s) is given after the collision is over. Match the condition of collision in column- with statements in column-. Column- Column- (A) Collision is perfectly elastic and head on (p) speed of both spheres after collision is u (B) Collision is perfectly elastic and oblique (q) velocity of both spheres after collision is different 1 (C) Coefficient of restitution is e = and (r) speed of both spheres after collision 2 collision is head on is same but less than u. 1 (D) Coefficient of restitution is e = and (s) speed of one sphere may be more than u. 2 collision is oblique STATEMENT-1 : Two spheres undergo a perfectly elastic collision. The kinetic energy of system of both spheres is always constant. [There is no external force on system of both spheres]. STATEMENT-2 : If net external force on a system is zero, the velocity of centre of mass remains constant. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True STATEMENT-1 : Non zero work has to be done on a moving particle to change its momentum. STATEMENT-2 : To change momentum of a particle a non zero net force should act on it. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True STATEMENT-1 : When a body collides elastically and head on with another identical stationary body on a frictionless surface, it losses all of its kinetic energy (No external forces on the system of the two bodies and no rotation of the bodies). STATEMENT-2 : In elastic collisions, only momentum is conserved. (a) If both assertion and reason are true and reason is the correct explanation of assertion (b) If both assertion and reason are true but reason is not the correct explanation of assertion. (c) If assertion is true but reason is false (d) If assertion is false but reason is true (A) a (B) b (C) c (D) d From a uniform square plate the shaded portions are removed as shown in figure. Find the coordinates of centre of mass of the remaining plate. X, Y axes and origin are shown in figure . In the figure shown two nonconducting blocks of A and B of mass ‘m’, 2m and charges – Q, 2Q respectively are attached at the two ends of a light spring of spring constant ‘k’. They are kept on a smooth horizontal surface. A and B are initially at rest and the spring is unstretched. Now a uniform electric field of intensity ‘E’ is switched on pointing towards right. Neglecting the electrostatic interaction between A and B find the maximum extension of the spring during the motion of the system. Also find the acceleration of ‘B’ at the moment of maximum extension in the spring A coordinate axis system taking x-axis as horizontal smooth floor is shown in figure. Two small balls of masses m and 3m attached with a string are released from some heights on y-axis as shown in figure. The balls may collide head on or obliquely. After a certain time mass m is at (9 cm, 20 cm) while mass 3m is 25 cm above the x axis and the strings is taut. The balls always remain in x-y plane. Find the length of string. A particle moving on a smooth horizontal surface strikes a stationary wall. The angle of strike is equal to the angle of rebound & is equal to 37° and 1 . Find the friction coefficient 5 X between wall and the particle in the form and fill value of X.: 10

the coefficient of restitution with wall is e =

37º 37º

////////////////////////////////////

24.

Answer Key (Revision Test - 05)

1.D 14. C

2. A 15. A

3. B 16. B

4. D 17. A

5. C 18. A

6. B 19. B

7. C 20. B

8. C 21. B

9. D 22. A

10. D 11. D 12. A 13. C,D 23. (A) q,r (B) p,s (C) p,s (D) p,s

8QE 55a 49a , 29. 3k 104 104 Solution will be provided with next revision test.

24. (A) p,q (B) p,q (C) q,r (D) q,r

RESONANCE

25. D

26. D

27. C

28.

30.

13 cm. 31. 5

4

REVISION TEST - 06 SUBJECT : PHYSICS COURSE : VIJAY (R) TOPIC : ROTATIONAL MOTION Time : 3 Hrs.

Max. Marks : 170

Instructions : 1. For each correct single choice question 3 marks (with 1 mark negative marking). 2. For each correct multipal choice question 3 marks (with 1 mark negative marking). 3. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking). 5. For each correct subjective question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

The moment of inertia of a thin sheet of mass M of the given shape about the specified axis is :

(A) 2.

7 Ma2 12

(B)

5 Ma2 12

(C)

R (B)

1 Ma2 12

(C)

2

R 2

(D)

R 4

A uniform ladder of length 5 m and mass 100 kg is in equilibrium between vertical smooth wall and rough horizontal surface. Find minimum friction co-efficient between floor and ladder for this equilibrium.

(A) 1/2 4.

(D)

A disc is hinged in a vertical plane about a point on its radius. What will be the distance of the hinge from the disc centre so that the period of its small oscillations under gravity is minimum? (A) R

3.

1 Ma2 3

(B) 3/4

(C) 1/3

(D) 2/3

Figure shows an arrangement of masses hanging from a ceiling. In equilibrium, each rod is horizontal, has negligible mass and extends three times as far to the right of the wire supporting it as to the left. If mass m4 is 48 kg then mass m1 is equal to :

m4 m3 m2 (A) 1 kg

RESONANCE

(B) 2 kg

(C) 3 kg

m1 (D) 4 kg

1

5.

A massless stick of length L is hinged at one end and a mass m attached to its other end. The stick is free to rotate in vertical plane about an fixed horizontal axis passing through frictionless hinge. The stick is held in a horizontal position. At what distance x from the hinge should a second mass M = m be attached to the stick, so that stick falls as fast as possible when released from rest. (A)

6.

(C) ( 2 1) L

3L

(D) ( 3 1) L

Two identical discs of mass m and radius r are arranged as shown in the figure. If is the angular acceleration of the lower disc and acm is acceleration of centre of mass of the lower disc, then relation between acm, & r is :

(A) acm = 7.

(B)

2L

r

(B) acm = 2

r

(C) acm = r

(D) none of these

A uniform rod of length l rotating with an angular velocity , while its centre moves with linear velocity v =

. If the end A of the rod is suddenly fixed, the 6

angular velocity of the rod will be : (A) 8.

(B)

3

(C)

2

(D)

2 3

A uniform disc of mass M and radius R is released from the shown position. PQ is a string, OP is a horizontal line, O is the centre of the disc and distance OP is R/2. Then tension in the string just after the disc is released will be :

(A) 9.

3 4

Mg 2

(B)

Mg 3

(C)

2Mg 3

(D) none of these

Mass m is connected with an ideal spring of natural length whose other end is fixed on a smooth horizontal table. Initially spring is in its natural length . Mass m is given a velocity ‘v’ perpendicular to the spring and released. The velocity perpendicular to the spring when its length is + x, will be

(A)

2v x

RESONANCE

(B)

2v 2 x

(C)

v x

(D) zero

2

10.

A uniform cubical solid block of side a moving with velocity v on a horizontal smooth plane as shown. It hits a fixed ridge at point O. The angular speed of the block just after it hits 'O' is

(A) 11.

v 3a

(C)

3v 2a

(D)

3v 4a

(B) r

(C) 3 r/2

(D) 2

Determine the acceleration a of the supporting surface required to keep the centre G of the circular pipe in a fixed position during the motion. No slipping takes place between pipe and its support.

(A) g sin 13.

v 2a

A uniform circular disc placed on a horizontal rough surface has initially a velocity v0 and an angular velocity 0 as shown in the figure. The disc comes to rest after moving some distance in the direction of motion. Then v0/0 is : (A) r/2

12.

(B)

(B) 2g sin

(C)

g sin 2

(D) 2 g sin

A solid sphere of mass m and radius r is gently placed on a conveyer belt moving with constant velocity V. If the coefficient of friction between the belt and sphere is

2 , the distance travelled by the centre of 7

the sphere before it starts pure rolling is

V2 (A) 7g 14.

2V 2 (C) 5g

2V 2 (D)

7g

A solid homogeneous cylinder of height h and base radius r is kept vertically on a conveyer belt moving horizontally with an increasing velocity v = a + bt2. If the cylinder is not allowed to slip then the time when the cylinder is about to topple, will be equal to (A)

15.

2V 2 (B) 49 g

rg bh

(B)

2 rg bh

(C)

2 bg rh

rg (D) 2 bh

A ring of mass m and radius R rolls on a horizontal rough surface without slipping due to an applied force ‘F’. The friction force acting on ring is :

(A)

F 3

RESONANCE

(B)

2F 3

(C)

F 4

(D) Zero

3

16.

A uniform disc of mass 2kg and radius 1m is mounted on an axle supported on fixed frictionless bearings. A light cord is wrapped around the rim of the disc and mass of 1kg is tied to the free end. If it is released from rest, (A) the tension in the cord is 5N (B) in first 4 seconds the angular displacement of the disc is 40 rad. (C) the work done by the torque on the disc in first 4 sec. is 200J (D) the increase in the kinetic energy of the disc in the first 4 seconds is 200J.

17.

Which of the following statements is/are true (A) work done by kinetic friction on an object may be positive. (B) A rigid body rolls up an inclined plane without sliding. The friction force on it will be upwards. (only contact force and gravitational force is acting) (C) A rigid body rolls down an inclined plane without sliding. The friction force on it will be upwards. (only contact force and gravitational force is acting) (D) A rigid body is left from rest from the top of a rough inclined plane. It moves down the plane with slipping. The friction force on it will be upwards.

Comprehension # 1 A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicycle wheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle is constant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown. Assume tension in the lower part of chain negligible. The cyclist is peddling at a constant rate of two revolutions per second. Assume that the force applied by other foot is zero when one foot is exerting 100 N force. Negelect friction within cycle parts & the rolling friction.

Chain upper part

F=100N

Gear 16cm

r=4cm

Sprocket Disc Wheel R=35cm

18.

19.

20.

21.

22.

The tension in the upper portion of the chain is equal to (A) 100 N (B) 120 N (C) 160 N

(D) 240 N

Net torque on the rear wheel of the bicycle is equal to (A) zero (B) 16 N-m (C) 6.4 N-m

(D) 4.8 N-m

The power delivered by the cyclist is equal to (A) 280 W (B) 100 W

(C) 64 W

(D) 32 W

The speed of the bicycle is : (A) 6.4 m/s (B) 3.5 m/s

(C) 2.8 m/s

(D) 5.6 m/s

The net force of the friction on the rear wheel due to the road is : (A) 100 N (B) 62 N (C) 32.6 N

(D) 18.3 N

Comprehension # 2 A square frame of mass m is made of four identical uniform rods of length L each. This frame is placed on an inclined plane such that one of its diagonals is parallel to the inclined plane as shown in figure, and is released.

RESONANCE

4

23.

The moment of inertia of square frame about the axis of the frame is : (A)

24.

(B)

2mL2 3

(C)

4mL2 3

(D)

mL2 12

The frictional force acting on the frame just after the release of the frame assuming that it does not slide is : (A)

25.

mL2 3

mg sin 3

(B)

2mg sin 7

(C)

3mg sin 5

(D)

2mg sin 5

The acceleration of the center of square frame just after the release of the frame assuming that it does not slide is : (A)

g sin 3

(B)

2 g sin 7

(C)

3 g sin 5

(D)

2 g sin 5

Comprehension # 3 A horizontal uniform rod of mass 'm' has its left end hinged to the fixed incline plane, while its right end rests on the top of a uniform cylinder of mass 'm' which in turn is at rest on the fixed inclined plane as shown. The coefficient of friction between the cylinder and rod, and between the cylinder and inclined plane, is sufficient to keep the cylinder at rest.

26.

The magnitude of normal reaction exerted by the rod on the cylinder is (A)

27.

mg 4

mg 3

(C)

mg 2

(D)

2 mg 3

The ratio of magnitude of frictional force on the cylinder due to the rod and the magnitude of frictional force on the cylinder due to the inclined plane is: (A) 1 : 1

28.

(B)

(B) 2 : 3

(C) 2 : 1

(D)

2 :1

The magnitude of normal reaction exerted by the inclined plane on the cylinder is: (A) mg

(B)

3 mg 2

(C) 2mg

(D)

5 mg 4

29.

STATEMENT-1 : A disc rolls without slipping on a fixed rough horizontal surface. Then there is no point on the disc whose velocity is in vertical direction. STATEMENT-2 : Rolling motion can be taken as combination of translation and rotation. Due to the translational part of motion a velocity (translational component) exist in horizontal direction for any point on the disc rolling on a fixed rough horizontal surface. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True.

30.

STATEMENT-1 : A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity. Then the acceleration of lowest point on the disc is zero. STATEMENT-2 : For a rigid disc rolling without slipping on a fixed rough horizontal surface, the velocity of the lowest point on the disc is always zero. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True.

RESONANCE

5

31.

STATEMENT-1 : A uniform cubical block(of side a) undergoes translational motion on a smooth horizontal surface under action of horizontal force F as shown. Under the given condition, the horizontal surface exerts normal reaction non-uniformly on lower surface of the block.

STATEMENT-2 : For the cubical block given in statement-1, the horizontal force F has tendency to rotate the cube about its centre in clockwise sense. Hence, the lower right edge of cube presses the horizontal surface harder in comparision to the force exerted by lower left edge of cube on horizontal surface. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. 32.

STATEMENT-1 : A homogeneous rectangular brick lies at rest on a fixed rough inclined plane as shown. Then the right half of the brick exerts greater force on the inclined plane as compared to left half of the brick.

STATEMENT-2 : For brick in situation of statement-1 to be at rest, the net moment of all forces about its centre of mass should be zero. Moment of force on brick due to its weight about centre of mass is zero. The moment of force due to friction on brick about its centre of mass has tendency to rotate the brick in clockwise sense. Hence the right half of the brick presses the inclined plane more in comparision to the left half of the brick. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True 33.

STATEMENT-1 : A body is purely rolling (rolling without slipping). The velocity of point of contact (of body) must be zero with respect to ground. STATEMENT-2 : By definition, pure rolling of a body occurs when velocity of its point of contact is zero relative to the surface on which it rolls. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

34.

Find out the moment of inertia of the following structure (written as thin uniform rods of mass per unit length .

RESONANCE

) about axis AB made of

6

35.

A circular hole of radius R/2 is cut from a thin uniform circular plate of radius R as shown (O is the centre of the circular plate). If the mass of the remaining plate is M, then find the moment of inertia of the plate about an axis through O perpendicular to plane of the plate ?

36.

In figure the uniform gate weighs 300 N and is 3 m wide & 2 m high. It is supported by a hinge at the bottom left corner and a horizontal cable at the top left corner, as shown. Find : (a)

the tension in the cable and

(b)

the force that the hinge exerts on the gate (magnitude & direction).

37.

The arrangement shown in figure consists of two identical uniform solid cylinders, each of mass m, on which two light threads are wound symmetrically. Find the tension of each thread in the process of motion. The friction in the axle of the upper cylinder is assumed to be absent.

38.

Two steel ball of equal diameter are connected by a rigid bar of negligible weight as shown and are dropped in the horizontal position from height h above the heavy steel and brass base plates. If the coefficient of restitution between the ball and steel base is 0.6 and that between the other ball and the brass base is 0.4. The angular velocity of the bar immediately after rebound is _______. Assume the two impacts are simultaneous. (g = 10 m/s 2)

39.

A ball of diameter d rolls without slipping along a horizontal smooth table top with constant speed v. The ball rolls off the edge falling to the floor a vertical distance h below. While in air the ball makes _______ revolutions.

40.

In the figure A & B are two blocks of mass 4 kg & 2 kg respectively attached to the two ends of a light string passing over a disc C of mass 40 kg and radius 0.1 m. The disc is free to rotate about a fixed horizontal axes, coinciding with its own axis. The system is released from rest and the string does not slip over the disc. Find:

(i) (ii) (iii)

the linear acceleration of mass B. the number of revolutions made by the disc at the end of 10 sec. from the start. the tension in the string segment supporting the block A. (g = 10 m/s 2)

RESONANCE

7

41.

A rigid cube ABCDEFGH is in motion. At a certain moment, face ABCD is vertical, and the velocities of vertices A and D are directed vertically downward and equal to v. At the same moment, the speed of point H equals 2v. What point of the cube has the maximum speed at that moment ? What is that speed ?

42.

A uniform ball of radius R rolls without slipping between two rails such that the horizontal distance is d between two contact points of the rail to the ball. If R=10cm, d=16cm and the angular velocity is 5rad/s velocity of centre of mass of the ball equals_____ [Pure rolling]

43.

A disk of mass M and radius R has a spring of constant k attached to its centre, the other end of the spring being fixed to a vertical wall. If the disk rolls without slipping on a level floor, how far to the right does the centre of mass move, if initially the spring was unstretched and the angular speed of the disk was o.

ANSWER KEY 1. 8. 15. 21. 28. 34.

A C D B B 13 3

2. 9. 16. 22. 29. 35.

37.

T = 1/10 mg

40.

(i) 10/13 m/s2 (ii) 5000/26 p (iii) 480/13 N

42.

0.3 m/sec

RESONANCE

B 3. C 10. A,B,C,D D 23. A B 30. 13/24 MR2 38.

43.

D D 17. 24. D 36.

0.28 rad/sec

4. A 5. C 6. B 11. A 12. A 13. A A,B,C,D 18. C 19. A D 25. C 26. C 27. 31. C 32. A 33. D (a) T = 225N, (b) FX = 225N, FY = 300N 39.

v d 41.

7. 14. 20. A

C A C

2h g vmax = 2L 2 L2 =

5 L

R o3m/2k)

8

REVISION TEST - 07 Course : VIJAY (R) TOPIC : ELECTROSTATICS Time : 3 Hrs.

Max. Marks : 170

Instructions : 1. For each correct Single choice question 3 marks (with 1 mark negative marking). 2. For each correct Multiple choice question 4 marks (with 1 mark negative marking). 3. For each correct answer in Comprehension 4 marks (with 1 mark negative marking). 4. For each correct Assertion/Reason question 3 marks (with 1 mark negative marking). 5. For each correct Subjective question 6 marks (with no negative marking). 6. For each correct Match the column question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

Five styrofoam balls are suspended from insulating threads. Several experiments are performed on the balls and the following observations are made : (i) Ball A repels C and attracts B. (ii) Ball D attracts B and has no effect on E. (iii) A negatively charged rod attracts both A and E. An electrically neutral styrofoam ball gets attracted if placed nearby a charged body due to induced charge. What are the charges, if any, on each ball ? A B C A B C D E (A) + – + 0 + (B) + – + + 0 D E (C) + – + 0 0 (D) – + – 0 0

2.

Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges of Q and – 3Q. They are suspended from two strings of same length fixed to points at the same horizontal level, but distant from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is (A) 2 (B) 3 (C) 1.5 (D) None of these

3.

A large sheet carries uniform surface charge density . A rod of length 2 has a linear charge density on one half and - on the second half. The rod is hinged at mid-point O and makes angle with the normal to the sheet. The electric force experienced by the rod is & (A) 0

4.

(B)

2 sin 2 0

(C)

2 sin (D) None of these 0

AB and CD are uniform line charges of infinite length having charge density 1 and 2 and lying along the z axis and y–axis respectively. The force between them depends on the perpendicular distance between them, 'r' as, F

(A) 0

RESONANCE

1. 2 2 0r n

, then the value of n is :

(B) 1/2

(C) 1

(D) 2

1

5.

A point charge – q is revolving in a circle of radius ' r ' around a fixed infinite line charge with positive charge per unit length. Now the point charge is shifted and it revolves in a circle of radius ' 2 r '. Then: (A) work done by all forces is zero (B) work done by electrical force is zero (C) work done by external force is zero (D) work done by all forces cannot be zero

6.

A ring carries a uniform linear charge density on one half and the linear charge density of same magnitude but opposite sign on the other half. (A) the component of electric field along the axis at all points on the axis is zero (B) the electric field along the axis and on the axis is zero only at the centre (C) the resultant field at the centre is zero (D) the resultant field at all points on the axis is zero. Two concentric rings, one of radius R and total charge +Q and the second of radius

7.

2R and total charge 8 Q, lie in x-y plane (i.e., z = 0 plane). The common centre of rings lies at origin and the common axis coincides with z-axis. The charge is uniformly distributed on both rings. At what distance from origin is the net electric field on z-axis zero. & (A) 8.

R 2

R (C)

2

2 2

(D)

2R

If the electric potential of the inner shell is 10 volt & that of the outer shell is 5 volt, then the potential at the centre will be: (the shells are uniformly charged)

(A) 10 volt 9.

R (B)

(B) 5 volt

(C) 15 volt

Find out work done by electric field in shifting a point charge

(D) 0 4 2 C from point P to S which are shown in 27

the figure :

(A) 10.

100 J 3

(B)

200 J 3

(C) 100 J

(D) 200 J

Figure shows three circular arcs, each of radius R and total charge as indicated. The net elecric potential at the centre of curvature is :

+Q 45° –2Q

•

30°

R +3Q

Q (A) 2 R 0

RESONANCE

Q (B) 4 R 0

2Q (C) R 0

Q (D) R 0

2

11.

Figure shows a solid hemisphere with a charge of 5 nC distributed uniformly through its volume. The hemisphere lies on a plane and point P is located on the plane, along a radial line from the centre of curvature at distance 15 cm. The electric potential at point P due to the hemisphere, is : P 15cm

(A) 150 V 12.

(B) 300 V

(B)

Qq / 4 0 mr

(C) 0

Qqm / 4 0 r

(D) cannot determine

A point mass ' m ' and charge ' q ' is projected with a velocity v towards a stationary charge Q0 from a distance of 2 m. The closest distance that q can approach is: [ k = 1/4 0 ]

(A) 14.

(D) 600 V

A charged particle of charge ‘Q’ is held fixed and another charged particle of mass ‘m’ and charge ‘q’ (of the same sign) is released from a distance ‘r’. The impulse of the force exerted by the external agent on the fixed charge by the time distance between ‘Q’ and ‘q’ becomes 2r is (A)

13.

(C) 450 V

mv 2 kqQ0 kQ0 q

(B)

kQ 0 2

mv k qQ 0

(C)

kQ 0 mv 2 k qQ 0

(D)

kQ 0 mv 2 k qQ 0

Two smooth spherical non conducting shells each of radius R having uniformly distributed charge Q & Q on their surfaces are released on a smooth non-conducting surface when the distance between their centres is 5 R. The mass of A is m and that of B is 2 m. The speed of A just before A and B collide

1 is: [Neglect gravitational interaction] (take K = 4 ) 0

(A) 15.

2 kQ 2 5 mR

(B)

4 kQ 2 5 mR

(C)

8 kQ 2 5 mR

(D)

16 kQ 2 5 mR

Four charges are rigidly fixed along the Y axis as shown. A positive charge approaches the system along the X axis with initial speed just enough to cross the origin. Then its total energy at the origin is

(A) zero 16.

(B) positive (C) negative (D) data insufficient p ˆ Two short dipoles p kˆ & k are located at (0, 0, 0) & (1 m, 0, 2 m) respectively. The resultant electric 2 field due to the two dipoles at the point (1 m, 0, 0) is : (A)

9p kˆ 32 0

RESONANCE

(B)

7p kˆ 32 0

(C)

7p kˆ 32 0

(D) none of these

3

17.

Total electric force on an electric dipole placed in an electric field of a point charge is: (A) always zero (B) never zero (C) zero when mid point of dipole coincides with the point charge (D) zero when dipole axis is along any electric line of force.

18.

A dipole of dipole moment p is kept at the centre of a ring of radius R and charge Q. The dipole moment has direction along the axis of the ring. The resultant force on the ring due to the dipole is: kPQ 2kPQ (A) zero (B) 3 (C) R R3 (D)

19.

kPQ

only if the charge is uniformly distributed on the ring

R3

For a system of two dipoles P1 and P2 as shown in the figure (both are at origin and perpendicular to each other along x and y axes respectively) (A) Work done in taking electron from P to R on QPR = 0 (B)

tan

(P1 P2 ) = 2 (P P ) 1 2

(C) tan

r

(P1 P2 ) = 2(P P ) 1 2

(D)

E .d r =

P1 P2 4 2 0 r 2

(P1 and P2 denotes magnitudes of P1 and P2 and r is quite large in comparison to dimensions of

dipoles, E is resultant electric field and QPR is a quarter of circle whose centre is at O) 20.

Two infinitely large charged planes having uniform surface charge density + and – are placed along x-y plane and yz plane respectively as shown in the figure. Then the nature of electric lines of forces in x-z plane is given by : z –

+

z

z

z

x (A)

21.

x

x (B)

z

x (C)

x (D)

Two equipotential spherical surfaces having potential 20 V and 0 V are as shown in figure. There is no charge anywhere in space except on the surface of both the spheres. Then which of the following figure represents the nature of electric field in region between the spherical surfaces by electric lines of forces. 0V

20V

(A)

RESONANCE

(B)

(C)

(D)

4

22.

A ring of radius R is placed in the plane with its centre at origin and its axis along the x-axis and having uniformly distributed positive charge. A ring of radius r ( 0. Neglect gravity. Find the time period.

38.

A point charge – q revolves around a fixed charge +Q in elliptical orbit. The minimum and maximum distance of – q from Q are r1 and r2 respectively. The mass of revolving particle is m. Qq > 0 and assume no gravitational effects. Find the angular momentum of q about Q .

39.

Find the magnitude of uniform electric field E in N/C (direction shown in figure) if an electron entering with velocity 100m/s making 30° comes out making 60° (see m figure), after a time numerically equal to of electron. e

40.

A solid sphere of radius ‘R’ is uniformly charged with charge density in its volume. A spherical cavity of radius

R is made in the sphere as shown in the figure. Find the electric 2

potential at the centre of the sphere. 41.

The arrangement shown consists of three elements

1. 2.

a thin rod of charge – 3.0 C that forms a full circle of radius 6.0 cm. a second thin rod of charge 2.0 C that forms a circular arc of radius 4.0 cm and concentric with the full circle, subtending an angle of 90° at the centre of the full circle. 3. an electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude 1.28 × 10–21 C-m. Find the net electric potential in volts at the centre.

42.

Electric field in a region is given by E 4 x ˆi 6 y ˆj . Then find the charge enclosed in the cube of side 1m oriented as shown in the diagram.

43.

A conducting sphere of radius R has two spherical cavities of radius a and b. The cavities have charges qa & qb respectively at their centres. ‘A’ is the centre of the sphere and ‘B’ is the centre of the cavity of radius ‘b’. Find : (i) electric field & electrical potential at (a) r (distance from A)> R, (b) r (distance from B)< b (ii) surface charge densities on the surface of radius R, radius a & radius b. (iii) What is the force on qa & qb?

RESONANCE

7

MATCH THE COLUMN 44.

Column gives a situation in which point charge(s) are placed at different position with respect to a uncharged thick conducting spherical shell. Column gives resulting effect. Match the figures in Column with the statements in Column . Column Column positive point charge q is placed at centre of shell

q

(A)

positive point charge q is placed inside gap of shell, but not at centre

q

(B)

(p)

charge is induced on inner surface of shell and is distributed uniformly

(q)

charge is induced on inner surface of shell and is distributed non-uniformly

(r)

charge is induced on outer surface of shell and is distributed uniformly

(s)

charge is induced on outer surface of shell and is distributed non-uniformly

q positive point charge q is placed outside the shell

(C)

(D)

A NS W ER S 1. 8. 15. 22. 29.

C A B C A

2. 9. 16. 23. 30.

C A B C B

3. 10. 17. 24. 31.

A A B B D

4. 11. 18. 25. 32.

A B B C D

5. 12. 19. 26. 33.

A B C C A

6. 13. 20. 27.

A B C AC

7. D 14. A 21. D 28. ABCD

6 q2

34.

4 0 a 2

35.

(a) 60º (b) mg +

kq1q2 2

stationary & q1q2 =

3 mg , mg . q1 & q2 should have unlike charges for the beads to remain

mg 2 k

md2 0 4 q

36.

4

37.

2

41.

0

42.

q = 2 0

38.

43.

Q q m r1 r2 2 0 (r1 r2 ) (i) (a)

Kqb Kqb Kqb K(qa qb ) – + ; E= 2 b r R r (A) p,r (B) q,r (C) s (D) q,s

(b) v = 44.

(c)

RESONANCE

v=

39.

100

5R 2 12 0

40.

K ( q a qb ) K(qa qb ) ; E= r r2

(ii) R =

qa qb 4R

2

, a =

qa 4 a

2

, b =

qb 4 b 2

(iii)

0

8

REVISION TEST - 08 Course : VIJAY (R) TOPIC : CAPACITANCE & CURRENT ELECTRICITY Time : 3 Hrs.

Max. Marks : 150

Instructions : 1. For each correct Single choice question 3 marks (with 1 mark negative marking). 2. For each correct Multiple choice question 3 marks (with 1 mark negative marking). 3. For each correct answer in Comprehension 4 marks (with 1 mark negative marking). 4. For each correct Assertion/Reason question 3 marks (with 1 mark negative marking). 5. For each correct Subjective question 6 marks (with no negative marking). 6. For each correct Match the column question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

The capacitance of a parallel plate capacitor will increase if: (A) a battery is connected to it (B) distance between the plates is increased (C) one plate is displaced parallel to itself by distance less than its length (D) none of these.

2.

A,B,C,D are large conducting plates kept parallel to each other. A and D are fixed. Plates B and C, connected to each other by a rigid conducting rod can slide over frictionless rails as shown. Initially the distance between plates A and B is same as that between plates C and D. If now the rod (along with plates B and C) is slightly moved towards right, the capacitance between the terminals 1 and 2. (A) remains unchanged (B) increases (C) decreases (D) nothing can be said

3.

The equivalent capacitance between x and y is:

(A) 4.

(B)

7 F 6

(C)

8 F 3

(D) 4 F

In the figure initial status of capacitor and their connection is shown. Which of the following is incorrect about this circuit :

(A) (B) (C) (D) 5.

5 F 6

Final charge on each capacitor will be zero Final total electrical energy of the capacitors will be zero Total charge flown from A to D is 30µC Total charge flown from A to D is – 30µC

A parallel plate capacitor of capacitance C (without dielectrics) is filled by dielectric slabs as shown in figure. Then the new capacitance of the capacitor is:

(A) 3.9 C

RESONANCE

(B) 4 C

(C) 2.4 C

(D) 3 C

1

6.

In the figure shown P1 and P2 are two conducting plates having charges of equal magnitude and opposite sign. Two dielectrics of dielectric constant K1 and K2 fill the space between the plates as shown in the figure. The ratio of electrical energy in 1st dielectric to that in the 2nd dielectric is (A) 1 : 1 (C) K2 : K1

7.

In the circuit shown the capacitor is initially uncharged. The charge passed through an imaginary circular loop parallel to the plates (also circular) and having the area equal to half of the area of the plates, in one time constant is:

(A) 0.63 C 8.

(B) K1 : K2 (D) K22 : K12

(B) 0.37 C

(C)

C

(D) zero

2

A graph between current & time during charging of a capacitor by a battery in series with a resistor is shown. The graphs are drawn for two circuits. R1, R2, C1, C2 and V1V2 are the values of resistance, capacitance and EMF of the cell in the two circuits. If only two parameters (out of resistance, capacitance, EMF) are different in the two circuits. What is /are the correct option(s) (A) V1 = V2; R1 > R2, C1> C2 (C) V1 < V2, R1< R2, C1 = C2

(B) V1 > V2, R1 > R2 ; C1 = C2 (D) V1 < V2, C1< C2, R1 = R2

9.

In the figure a capacitor of capacitance 2µF is connected to a cell of emf 20 volt. The plates of the capacitor are drawn apart slowly to double the distance between them. The work done by the external agent on the plates is : (A) – 200 µJ (B) 200 µJ (C) 400 µJ (D) – 400 µJ

10.

The plates S and T of an uncharged parallel plate capacitor are connected across a battery. The battery is then disconnected and the charged plates are now connected in a system as shown in the figure. The system shown is in equilibrium. All the strings and spring are insulating and massless. The magnitude of charge on one of the capacitor plates is: [ Area of plates = A ]

(A) 11.

2 m g A 0

(B)

4 m g A 0 k

(C)

m g A 0

(D)

2 m g A 0 k

In the capacitor discharge formula q = q0 e–t/ the symbol represents : (A) the time it takes for C to loose q0/e charge. 1 (B) the time it takes for C to loose charge q0 1 e (C) the time it takes for C to loose essentially all of its initial charge. (D) none of the above.

12.

A uniform wire of resistance R is stretched uniformly n times & then cut to form five identical wires. These wires are arranged as shown in the figure. The effective resistance between A & B will be:

(A)

nR 5

RESONANCE

R

(B)

5n

2

(C)

n2 R 5

(D)

n2 R 2

2

Conductivity

(C) Conductivity

(D) Conductivity

Resistivity

(B)

Resistivity

(A)

Resistivity

Which graph best represent the relationship between conductivity and resistivity for a solid ? Resistivity

13.

Conductivity

14.

A battery of internal resistance 2 is connected to a variable resistor whose value can vary from 4 to 10 . The resistance is initially set at 4 If the resistance is now increased then (A) power consumed by it will decrease (B) power consumed by it will increase (C) power consumed by it may increase or may decrease (D) power consumed will first increase then decrease.

15.

The resistance of each arm in the circuit shown in figure has same value. (i.e. R12 = R10 = R13 = R2O = R24 = ..... etc.). The ratio Q12/Q34 of the amounts of heat liberated per unit time in conductors 1-2 and 3-4 is : (A) 4 : 1 (B) 8 : 1 (C) 16 : 1 (D) none of these

16.

In the circuit shown the variable resistance X is to be adjusted such that the ideal ammeter reads the same in both the positions of the key, when connected independently to 1 and then to 2. The reading of the ammeter is 2A. If E = 10 V, then x is : (A) 5. (B) 20 (C) 50 (D) cannot be determined

17.

In the diagrams, all light bulbs are identical and all emf sources are ideal and identical. In which circuit (given in options) will each bulb glow with the same brightness as in the circuit shown ?

(A)

18.

19.

(B)

(C)

(D)

In the circuit shown in figure, the resistance of voltmeter is 6 K. The voltmeter reading will be : (A) 6V

(B) 5V

(C) 4V

(D) 3V

In a practical wheat stone bridge circuit as shown, when one more resistance of 100 is connected in parallel with unknown resistance ' x ', then ratio 1/2 become ' 2 '. 1 is balance length. AB is a uniform wire. Then value of ' x ' must be: copper strips (rk¡ csd h ifê;k¡ ) 100

x G

A 1

2 E

(A) 50

RESONANCE

(B) 100

B copper strips (rk¡ csd h ifê;k¡ )

r

(C) 200

(D) 400

3

MULTIPLE CHOICE QUESTIONS 20.

Charged particles with different charge to mass ratios are projected into the region of space between the plates of a parallel plate capacitor with velocities directed parallel to the plates. All particles have received their initial kinetic energy by passing the same potential difference V0. The potential difference across the capacitor plates is V, and the distance between the plates is d. If all the particles are projected from a point that is exactly in the middle of the distance between the plates and '' is the distance travelled (along the direction of initial velocity) by any particle before hitting any of the plate, then is dependent as (neglect the interaction among the particles and effect of induction) :

d

(A) V0 21.

(B)

q m

(C)

1

(D) d

V

Two capacitors C 1 & C 2 are charged to same potential V, but with opposite polarity as shown in fig. The switch S 1 & S 2 are then closed.

(A)P.d. across two capacitors are same & is given by

(C1 C 2 )V (C1 C 2 )

C1V (B)P.d. across two capacitors are same & is given by (C C ) 1 2

(C1 C 2 ) (C)Ratio of final energy to initial energy of the system is (C1 C 2 )

2

(C1 ) (D)Ratio of final energy to initial energy of the system is 2 (C1 C2 ) 22.

The figure shows, a graph of the current in a discharging circuit of a capacitor through a resistor of resistance 10 . (A) The initial potential difference across the capacitor is 100 volt.

1 (B) The capacitance of the capacitor is 10 n 2 F.. (C) The total heat produced in the circuit will be

500 joules. n2

(D) The thermal power in the resistor will decrease with a time constant 23.

1 second. 2 n2

In the figure a conductor of nonuniform cross-section is shown. A steady current flows in it. (A) The electric field at A is more than at B. (B) The electric field at B is more than at A. (C) The thermal power generated at A is more than at B in an element of small same width. (D) The thermal power generated at B is more than at A in an element of small same width.

RESONANCE

4

COMPREHENSION Comprehension The circuit contains ideal battery E and other elements arranged as shown. The capacitor is initially uncharged and switch S is closed at t = 0. (use e2 = 7.4)

24.

Time constant of the circuit is (A) 48 s (B) 28.8 s

(C) 72 s

(D) 120 s

25.

The potential difference across the capacitor in volts, after two time constants, is approximately : (A) 2 (B) 7.6 (C) 10.4 (D) 12

26.

The potential difference across resistor R1 after two time constants, is approximately : (A) 1.6 V (B) 7.6 V (C) 10 V (D) 12 V

27.

The potential difference across resistor R2 after two time constants, is : (A) 2V

(B) 7.6V

(C) 10V

(D) 12 V

Comprehension In the circuit shown below, the internal resistance of the cell is negligible. The distance of the slider from the left-hand end of the slide wire is . The graph shows the variation with of the current in the cell.

+

–

6.00 V d.c. 100 cm Slider

100 cm slider wire

R Cell

28.

29.

Centre zero milliammeter

The balance point is at length l that is equal to (A) 0 cm (B) 20 cm

(C) 30 cm

(D) 40 cm

E.M.F. of the cell is : (A) 0.98 V

(C) 1.86 V

(D) 2.00 V

(B) 1.20 V

ASSERTION / REASON 30.

STATEMENT-1 : A dielectric is inserted between the plates of an isolated fully-charged capacitor. The dielectric completely fills the space between the plates. The magnitude of electrostatic force on either metal plate decreases, as it was before the insertion of dielectric medium. STATEMENT-2 : Due to insertion of dielectric slab in an isolated parallel plate capacitor (the dielectric completely fills the space between the plates), the electrostatic potential energy of the capacitor decreases. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True.

RESONANCE

5

31.

STATEMENT-1 : When an external resistor of resistance R (connected across a cell of internal resistance r) is varied, power consumed by resistance R is maximum when R = r. STATEMENT-2 : Power consumed by a resistor of constant resistance R is maximum when current through it is maximum. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

SUBJECTIVE CHOICE QUESTIONS 32.

Find the equivalent capacitance between terminals ‘A’ and ‘B’. The letters have their usual meaning.

33.

Find the equivalent resistance of the circuit as shown in the figure between the junctions A and B. Each of the twelve wires have a resistance R ohms .

34.

(a)

In the circuit shown the resistance ‘R’ can be varied. Plot the graph of current through ‘R’ against R.

(b)

In the figure shown ‘R’ can be varied. Find the value of ‘R’ so that electric power consumed by it becomes maximum.

35.

Two potentiometer wires w1 and w2 of equal length connected to a battery of emf P and internal resistance ' r ' through two switches s 1 and s 2. A battery of emf is balanced on these potentiometer wires. If potentiometer wire w1 is of resistance 2r and balancing length is /2 when only s 1 is closed

2 , then find 3

and s 2 is open. On closing s 2 and opening s 1 the balancing length on w2 is found to be the resistance of potentiometer wire w2.

RESONANCE

6

MATCH THE COLUMN 36.

Column I gives physical quantities of a situation in which a current i passes through two rods I and II of equal length that are joined in series. The ratio of free electron density (n), resistivity () and cross-section area (A) of both are in ratio n1 : n2 = 2 : 1, 1 : 2 = 2 : 1 and A1 : A2 = 1 : 2 respectively. Column II gives corresponding results. Match the ratios in Column with the values in Column .

i A

B

C

Column

37.

Column

(A)

Drift velocity of free electron in rod Drift velocity of free electron in rod

(p) 0.5

(B)

Electric field in rod Electric field in rod

(q) 1

(C)

Potential difference across rod Potential difference across rod

(r) 2

(D)

Average time taken by free electron to move from A to B Average time taken by free electron to move from B to C

(s) 4

Match the readings of the voltmeter and ammeter respectively shown in the figures. Column Column

3

(a) 7V

24V

(P) 0V

3

7V

24V

(b)

V

7V

(Q) 20A

3 24V

(c)

7V

(d)

RESONANCE

(R) 0A

3 24V A

(S) 20 V

7

38.

Column I gives certain situations in which capacitance of a capacitor is changed by different means. Column II gives resulting effect under different conditions. Match the statements in column I with the corresponding statements in column II. Column I Column II (A) The plates of a plane parallel capacitor are (p) Increases if the capacitor is maintained slowly pulled apart. Then the magnitude of at constant charge. electric field intensity inside the capacitor. (B) The plates of a plane parallel plate capacitor (q) Decreases if the capacitor is are slowly pulled apart. Then the potential maintained at constant charge energy stored in the capacitor. (C) The capacitance of an air filled plane parallel (r) Increases if the capacitor is maintained plate capacitor on insertion of dielectric at constant potential difference. (D) A dielectric slab is inserted inside an air (s) Decreases if the capacitor is maintained filled plane parallel plate capacitor. The at constant potential difference. potential energy stored in the capacitor.

39.

Two identical capacitors are connected in series, and the combination is connected with a battery, as shown. Some changes in the capacitor 1 are now made independently after the steady state is achieved, listed in column-I. Some effects which may occur in new steady state due to these changes on the capacitor 2 are listed in column-II. Match the changes one capacitor 1 in column-I with corresponding effect on capacitor 2 in column-II.

+ _

Cap.1

Cap.2

Column I (A) A dielectric slab is inserted. (B) Separation between plates increased. (C) A metal plate is inserted connecting both plates (D) The left plate is grounded.

Column II (p) Charge on the capacitor increases. (q) Charge on the capacitor decreases. (r) Energy stored in the capacitor increases. (s) No change is occured.

ANSWERS 1.

D

2.

A

3.

D

4.

C

5.

A

6.

C

7.

D

8.

C

9.

B

10.

A

11.

B

12.

C

13.

C

14.

A

15.

C

16.

A

17.

C

18.

B

19.

B

20.

ACD

21.

AC

22.

ABCD 23.

AC

24.

A

25.

C

26.

A

27.

D

28.

B

29.

B

D

31.

B

32.

13 0 A 10 d

33.

Req =

34.

(a) R = 0 , (b)

37.

(a) P (b) P (c) R (d) R 38.

30.

RESONANCE

R=

r 35. 2

2R R = 4 2

From (1) & (2) R = r

36.

(A) q (B) s (C) s (D) q

(A) s (B) p, s (C) p, r (D) q, r

39.

(A) p, r (B) q (C) p,r (D) s

8

REVISION TEST - 09 Course : VIJAY (R) TOPIC : EMF Time : 3 Hrs.

Max. Marks : 117

Instructions : 1. For each correct Single choice question 3 marks (with 1 mark negative marking). 2. For each correct Multiple choice question 3 marks (with 1 mark negative marking). 3. For each correct answer in Comprehension 4 marks (with 1 mark negative marking). 4. For each correct Assertion/Reason question 3 marks (with 1 mark negative marking). 5. For each correct Subjective question 6 marks (with no negative marking). 6. For each correct Match the column question 6 marks (with no negative marking).

SINGLE CHOICE QUESTIONS 1.

An electron (charge e, mass ' m ' ) is revolving around a fixed proton in circular path of radius ' r '. The magnetic field at the centre due to electron is: (A) 0

0 e2

(B)

8r 2.

3.

2

m0 r

0 e

(C)

0 e

(D)

8 r m0 r

4r

2

m0 r

A point charge is moving in clockwise direction in a circle with constant speed. Consider the magnetic field produced by the charge at a point P (not centre of the circle) on the axis of the circle. (A) it is constant in magnitude only (B) it is constant in direction only (C) it is constant in direction and magnitude both (D) it is not constant in magnitude and direction both. A particle is moving with velocity v ˆi 3ˆj and it produces an electric field at a point given by E 2kˆ . It will produce magnetic field at that point equal to (all quantities are in S.. units) (A)

4.

6 ˆi 2ˆj c2

(B)

6ˆi 2ˆj c2

(C) zero

(D) can not be determined from the given data

Two observers moving with different velocities see that a point charge produces same magnetic field at the same point A . Their relative velocity must be parallel to r , where r is the position vector of point A with respect to point charge. This statement is : (A) true (B) false (C) nothing can be said (D) true only if the charge is moving perpendicular to the r

5.

A uniformly charged ring of radius R is rotated about its axis with constant linear speed v of each of its particles. The ratio of electric field to magnetic field at a point P on the axis of the ring distant x = R from centre of ring is (c is speed of light)

(A)

6.

c2 v

(B)

v2 c

(C)

c v

(D)

v c

(D)

2 0 d

If the magnetic field at 'P' can be written as K tan then K is : 2

[Refer to the figure of question no. 8] (A)

0 4d

RESONANCE

(B)

0 2d

(C)

0 d

1

7.

The magnetic field at the origin due to the current flowing in the wire is

(A)

0 ˆ ˆ (i k) 8 a

(B)

0 ˆ ˆ (i k) 2 a

(C)

0 ˆ ˆ ( i k) 8 a

(D)

0 4a 2

8.

A negative charge is given to a loop and the loop is rotated in the plane of paper about its centre as shown. The magnetic field produced by the ring affects a small magnet placed above the ring in the same plane of paper. (A) the magnet does not rotate (B) the magnet rotates clockwise as seen by observer from below (C) the magnet rotates anti-clockwise as seen from below (D) none of the above.

9.

A nonconducting disc having uniform positive charge Q, is rotating about its axis with uniform angular velocity . The magnetic field at the center of the disc is.

10.

(A) directed outward

0Q (B) having magnitude 4 R

(C) directed inwards

0Q (D) having magnitude 2 R

( ˆi kˆ )

A uniform circular loop of radius a and resistance R is pulled at a constant velocity v out of a region of uniform magnetic field whose magnitude is B. The plane of loop and the velocity are both perpendicular to B . Then the electrical power in the circular loop at the instant when the arc (of circular loop) outside the region of magnetic field subtends an angle at centre of the loop is : 3

B 2a 2 v 2 2B 2a 2 v 2 B 2a 2 v 2 (B) (C) (D) None of these R R 2R An electron moving with velocity V along the axis approaches a circular current carrying loop as shown in the figure. The magnitude of magnetic force on electron at this instant is

(A) 11.

(A)

0 e v iR 2 x 2 ( x 2 R 2 )3 / 2

RESONANCE

(B) 0

e v iR 2 x ( x 2 R 2 )3 / 2

(C)

0 e v iR 2 x 4 ( x 2 R 2 )3 / 2

(D) 0

2

12.

q is entering in a magnetic field of strength B at a m speed v = (2d)(B), then which of the following is correct : If a charged particle of charge to mass ratio

(A) (B)

(C) (D) 13.

14.

angle subtended by charged particle at the centre of circular path is 2. the charge will move on a circular path and will come out from magnetic field at a distance 4d from the point of insertion. 2 the time for which particle will be in the magnetic field is . B the charged particle will subtend an angle of 900 at the centre of circular path

A proton moves in the positive z-direction after being accelerated from rest through a potential difference V. The proton then passes through a region with a uniform electric field E in the positive x-direction and a uniform magnetic field B in the positive y-direction, but the proton's trajectory is not affected. If the experiment were repeated using a potential difference of 2V, the proton would then be (A) deflected in positive x-direction (B) deflected in negative x-direction (C) deflected in positive y-direction (D) deflected in negative y-direction In region x > 0, a uniform and constant magnetic field B1 2 B 0 kˆ exists. Another uniform and constant magnetic field B 2 B 0 kˆ exists in region x < 0. A positively charged particle of mass m and charge q is crossing origin at time t = 0 with a velocity u u 0 ˆi . The particle comes back to its initial position after a time : (B0, u0 are positive constants)

3 m (A) 2 q B 0

2m (B) qB 0

3m (C) qB 0

(D) Particle does not come back to its initial position. 15.

16.

Figure shows an equilateral triangle ABC of side carrying currents, placed in uniform magnetic field B. The magnitude of magnetic force on triangle is : (A) iB

(B) 2 iB

(C) 3iB

(D) zero

Two long wires which are perpendicular to each other carry currents as shown in the figure. They are free to move. Consider only magnetic interaction

(A) the two wires will come closer transitionally (B) the two wires will move away transitionally (C) the two wires will rotate such that the currents become uni-directional and then come closer due to attraction (D) the two wires will rotate such that the currents become anti-parallel and then move far away due to repulsion.

RESONANCE

3

17.

A uniform, constant magnetic field B is directed at an angle of 45° to the x-axis in the xy-plane, PQRS is a rigid square wire frame carrying a steady current 0, with its centre at the origin O. At time t = 0, the frame is at rest in the position shown in the figure, with its sides parallel to the x and y axes. Each side of the frame is of mass M and length L.

The torque about O acting on the frame due to the magnetic field will be

(A) =

B 0L2 2

2 B L ˆi ˆj i j (B) = 0

2

(C) =

B 0L2 2

ˆi ˆj (D) =

B 0L2 2

ˆi ˆj

MULTIPLE CHOICE QUESTIONS 18.

A single circular loop of wire with radius 0.02 m carries a current of 8.0 A. It is placed at the centre of a solenoid that has length 0.65 m, radius 0.080 m and 1300 turns. Solenoid

Current carrying loop

(A) The value of the current in the solenoid so that the magnetic field at the centre of the loop becomes zero, is equal to 44 mA. (B) The value of the current in the solenoid so that the magnetic field at the centre of the loop becomes zero, is equal to 100 mA. (C) The magnitude of the total magnetic field at the centre of the loop (due to both the loop and the solenoid) if the current in the loop is reversed in direction from that needed to make the total field equal to zero tesla, is 8 x 10–5 T. (D) The magnitude of the total magnetic field at the centre of the loop (due to both the loop and the solenoid) if the current in the loop is reversed in direction from that needed to make the total field equal to zero tesla, is 16 x 10–5 T. 19.

A particle of charge ‘q’ & mass ‘m’ enters normally (at point P) in a region of magnetic field with speed v. It comes out normally from Q after time T as shown in figure. The magnetic field B is present only in the region of radius R and is uniform. Initial and final velocities are along radial direction and they are perpendicular to each other. For this to happen, which of the following expression(s) is/are correct : (A) B =

mv qR

(B) T =

R 2v

(C) T =

m 2qB

(D) None of these

20.

Figure shows the path of an electron in a region of uniform magnetic field. The path consists of two straight sections, each between a pair of uniformly charged plates, and two half circles. The electric field exists only between the plates. (A) Plate I of pair A is at higher potential than plate-II of the same pair. (B) Plate I of pair B is at higher potential than plate II of the same pair. (C) Direction of the magnetic field is out of the page [ ]. (D) Direction of the magnetic field in to the page [ ].

RESONANCE

Pair-A

Pair-B

4

COMPREHENSION Comprehension

As a charged particle ‘q’ moving with a velocity v enters a uniform magnetic field B , it experiences a force F = q (v B ) . For = 0º or 180º, being the angle between v and B , force experienced is zero and the particle passes undeflected. For = 90º, the particle moves along a circular arc and the magnetic force mv 2 . For other values of ( 0º, 180º, 90º), the charged (qvB) provides the necessary centripetal force r particle moves along a helical path which is the resultant motion of simultaneous circular and translational motions. Suppose a particle, that carries a charge of magnitude q and has a mass 4 × 10–15 kg, is moving in a region containing a uniform magnetic field B = – 0.4 kˆ T. At some instant, velocity of the particle is v =

(8iˆ 6 ˆj 4kˆ) × 106 m/s and force acting on it has a magnitude 1.6 N. 21.

Motion of charged particle will be along a helical path with : (A) A translational component along x-direction and a circular component in the y-z plane (B) A translational component along y-direction and a circular component in the x-z plane (C) A translational component along z-axis and a circular component in the x-y plane (D) Direction of translational component and plane of circular component are uncertain

22.

Angular frequency of rotation of particle, also called the ‘cyclotron frequency’ is : (A) 8 × 105 rad/s (B) 12.5 × 104 rad/s (C) 6.2 × 106 rad/s (D) 4 × 107 rad/s

23.

If the coordinates of the particle at t = 0 are (2 m, 1 m, 0), coordinates at a time t = 3 T, where T is the time period of circular component of motion, will be (take = 3.14) : (A) (2 m, 1 m, 400 m) (B) (0.142 m, 130 m, 0) (C) (2 m, 1 m, 1.884 m) (D) (142 m, 130 m, 628 m)

ASSERTION / REASON 24.

Statement 1 : A direct uniformly distributed current flows through a solid long metallic cylinder along its length. It produces magnetic field only outside the cylinder . Statement 2 : A thin long cylindrical tube carrying uniformly distributed current along its length does not produce a magnetic field inside it. Moreover, a solid cylinder can be supposed to be made up of many thin cylindrical tubes. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

25.

STATEMENT-1 : A pendulum made of an insulated rigid massless rod of length is attached to a small sphere of mass m and charge q. The pendulum is undergoing oscillations of small amplitude having time period T. Now a uniform horizontal magnetic field B out of plane of page is switched on. As a result of this change, the time period of oscillations does not change.

STATEMENT-2 : A force acting along the string on the bob of a simple pendulum (such that tension in string is never zero) does not produce any restoring torque on the bob about the hinge. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

RESONANCE

5

26.

STATEMENT–1 : No electric current will be present within a region having uniform and constant magnetic field. STATEMENT–2 : W ithin a region of uniform and constant magnetic field B , the path integral of magnetic field B d along any closed path is zero. Hence from Ampere circuital law B d o I

(where the given terms have usual meaning), no current can be present within a region having uniform and constant magnetic field. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True.

SUBJECTIVE CHOICE QUESTIONS 27.

A thin beam of charged particles is incident normally on the boundary of a region containing a uniform magnetic field as shown. The beam comprise of monoenergetic and – particles, each possessing a kinetic energy T. Neglecting interaction between particles of the beam, find the separation between the and particles when they emerge out of the magnetic field. (express your answer in terms of T, B, e, me & m, where all terms have their usual meanings.) (Te T )

28.

The given fig. shows a coil bent with AB = BC = CD = DE = EF = FG = GH = HA = 1 m and carrying current 1 A. There exists in space a vertical uniform magnetic field of 2 T in the y-direction. Then find out the torque (in vector form) on the loop.

MATCH THE COLUMN 29.

A beam consisting of four types of ions A, B, C and D enters a region that contains a uniform magnetic field as shown. The field is perpendicular to the plane of the paper, but its precise direction is not given. All ions in the beam travel with the same speed. The table below gives the masses and charges of the ions. Region containing Magnetic field

1

2

3 r4

r2

r1 Ion beam

RESONANCE

4

r3

ION A B C D

MASS 2m 4m 2m m

CHARGE e –e –e +e

r4 > r3 = r2 > r1

6

The ions fall at different positions 1, 2, 3 and 4, as shown. Correctly match the ions with respective falling positions.

30.

Column

Column

(a) A

(P) 1

(b) B

(Q) 2

(c) C

(R) 3

(d) D

(S) 4

A charged particle having non zero velocity is subjected to certain conditions given in Column . Column gives possible trajectories of the particle. Match the conditions in column with the results in Coulmn Column

31.

Column

(A)

In only uniform electric field

(p) the path of the charged particle may be a straight line

(B)

In only uniform magnetic field

(q) the path of the charged particle may be a parabola

(C)

In uniform magnetic and uniform electric field such that both are parallel

(r) the path of the charged particle may be a circle

(D)

Subjected to a net force of constant magnitude

(s) the path of the charged particle may be a helix with uniform or non uniform pitch

A uniform and constant magnetic field exists in whole space as shown by magnetic lines of forces. Each of the four particles 1, 2, 3 and 4 have charge +q and mass m. Each of the particle is given a initial velocity of magnitude 'v '; the angle between initial velocity of each particle and magnetic field is shown (velocity of particle 2 is along the magnetic field and velocity of particle 4 is perpendicular to magnetic field). Neglect electrostatic and magnetic force on each charge due to remaining three charges. Match the statements in column-I with particle(s) they correspond to in column-II.

Column-I

Column-II

(A)

The magnitude of angle between velocity and magnetic field does not change for

(p) Particle 1

(B)

Total distance travelled in time 't' is equal to 'vt ' for

(q) Particle 2

(C)

The magnitude of acceleration is non zero and constant for

(r) Particle 3

(D)

If a uniform electric field is switched on in direction of existing magnetic field, the name of the path of trajectory becomes different for

(s) Particle 4

RESONANCE

7

32.

A square wire frame ABCD is made of four thin uniform rods of length 'a' each. The charge per unit length on each of four rods is uniform and . The frame moves in x-y plane (z = 0 plane) with constant velocity v v 0 ˆi , the centre of frame always lies on x-axis and side BC is parallel to y-axis. At the instant centre of frame is at origin, match the positions in column- with respective nature of fields in column-II.

Column-I

Column-II

(A) At point P whose coordinates are (4a, 0, 0)

(p) magnitude of magnetic field is zero

(B) At point Q whose coordinates are (0, 4a, 0)

(q) magnitude of magnetic field is nonzero

(C) At point R whose coordinates are (0, 0, 4a)

(r) magnitude of electrostatic field is zero

(D) At origin

(s) magnitude of electrostatic field is nonzero

ANSWERS 1.

B

2.

A

3.

A

4.

A

5.

A

6.

B

7.

C

8.

B

9.

AD

10.

A

11.

D

12.

B

13.

B

14.

B

15.

A

16.

C

17.

A

18.

BD

19.

ABC

20.

ABC

21.

C

22.

D

23.

C

24.

D

25.

A

26.

A

27.

2 2T m m e eB 2

28.

2 kˆ units

29.

(a) S (b) P (c) Q (d) R

30.

(A) p, q ; (B) p, r, s ; (C) p, s ; (D) p, q, r, s

31.

(A) p,q,r,s, (b) p,q,r,s, (c) p,r,s (d) s

32.

(A) p,s (B) q,s (C) q,s (D) p,r

RESONANCE

8

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