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Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [1]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A raindrop of radius r falls from a certain height h above the ground. The work done by the gravitational force is proportional to : (A) r (B) r2 (C) r3 (D) r4

2.

When a spring is stretched by an amount x, the potential energy stored in it is V. When the same spring is stretched by an amount 2x, the potential energy stored in it will be : (A) V/2 (B) 2V (C) V/4 (D) 4V

3.

A pendulum has a length l. Its bob is pulled aside from its equilibrium position through an angle and then released. The speed of the bob when it passes through the equilibrium position is given by : (A)

2gl

(B)

2gl cos

(C)

2 gl 1 cos

(D)

2 gl 1 sin

4.

A moving bullet hits a solid target resting on a frictionless surface and gets embedded in it. What is conserved in this process ? (A) momentum and kinetic energy (B) kinetic energy alone (C) momentum alone (D) neither momentum nor kinetic energy

5.

Two identical balls marked 2 and 3, in contact with each other and at rest on a horizontal frictionless table, are hit head-one by another identical ball marked 1 moving initially with a speed v as shown in figure. What is observed, if the collision is elastic ?

(A) (B) (C) (D) 6.

The bob A of a pendulum released from a height h hits head-on another bob B of the same mass of an identical pendulum initially at rest. What is the result of this collision ? Assume the collision to be elastic (see figure).

(A) (B) (C) (D) 7.

Ball 1 comes to rest and balls 2 and 3 roll out with speed v/2 each Ball 1 and 2 come to rest and ball 3 roll out with speed v Balls 1, 2 and 3 roll out with speed v/3 each Balls 1, 2 and 3 come to rest

Bob A comes to rest at B and bob B moves to the left attaining a maximum height h Bobs A and B both move to the left, each attaining a maximum height h/2 Bob B moves to the left and bob A moves to the right, each attaining a maximum height h/2 Both bobs come to rest

A steel ball falls from a height h on a floor for which the coefficient of restitution is e. The height attained by the ball after two rebounds is : (A) eh (B) e2h (C) e3h (D) e4h

VMC/Energy & Momentum

28

HWT/Physics

Vidyamandir Classes 8.

For a head-on collision between two balls, velocities are exchanged if : (A) collision is elastic (B) balls have same radius (C) balls have same mass (D) both (A) and (C) together

9.

In figure, if M > m, the number of collisions between the balls will be :

(A) 10.

one

(B)

two

(C)

three

(D)

four

A body of mass m = 1 kg is dropped from a height h = 40 cm on a horizontal platform fixed to one end of an elastic spring, the other being fixed to a base. As a result the spring is compressed by an amount x = 10 cm. What is the force constant of the spring. Take = g 10 ms 2 . (A)

600 Nm 1

VMC/Energy & Momentum

(B)

800 Nm 1

(C)

29

1000 Nm 1

(D)

1200 Nm 1

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [2]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A body of mass 5 kg is moving along the x-axis with a velocity 2 ms 1 . Another body of mass 10 kg is moving along the y-axis with a velocity (A)

2.

3.

3ms 1 . They collide at the origin and stick together. The final velocity of the combined mass is :

3 ms 1

(B)

3 1 ms 1

(C)

4 1 ms 3

(D)

None

A spacecraft of mass M explodes into two parts when its velocity is V. After the explosion, one part of mass m is left stationary. What is the velocity of the other part ? MV MV MV mV (A) (B) (C) (D) m M m M m M m

A body of mass 2 kg moving with a velocity ˆi 2 ˆj 3kˆ ms 1 collides with another body of mass 3 kg moving with a velocity

2ˆi ˆj kˆ in ms . If they stick together, the velocity in ms 1 ˆ (A) 8i 7 ˆj 3kˆ (B) 15 4ˆi ˆj 3kˆ (C) 5 1

1

of the composite body is :

1 ˆ ˆ ˆ 8i j k 5

(D)

1 4ˆi 7 ˆj 3kˆ 5

4.

Two equal spheres A and B lie on a smooth horizontal circular groove at opposite ends of a diameter. Sphere A is projected along the groove and at the end of time T impinges on sphere B. If e is the coefficient of restitution, the second impact will occur after a time equal to : 2T (A) T (B) eT (C) (D) 2eT e

5.

Two masses M and m (with M > m) are connected by means of a pulley as shown in figure. The system is released. At the instant when mass M has fallen through a distance h, the velocity of mass m will be : (A)

(C)

2gh

2gh M m

M m

VMC/Energy & Momentum

(B)

(D)

2gh M m

2gh M m

M m

30

HWT/Physics

Vidyamandir Classes 6.

A mass m, lying on a horizontal frictionless surface is connected to mass M as shown in figure. The system is now released. The velocity of mass m when mass M is descended a distance h is : (A) (C)

7.

2Mgh

M m

(B)

2mgh M

(D)

2gh

A uniform rope of length L is lying in a lump on a frictionless table. A small part of the rope is held hanging through a hole in the table just below the lump. The system is then released. The speed of the end of the rope as it leaves the hole is : (A)

8.

2Mgh m

(B)

gL

2

gL 3

(C)

2 gL 3

(D)

zero

A bullet of mass m is fired horizontally with a velocity v on a wooden block of mass M suspended from a support and gets embedded in it. The kinetic energy of the bullet + block system is : (A)

1 2 mv 2

1 M m v2 2

(B)

(C)

Mmv 2 2 M m

(D)

m2v 2 2 M m

Paragraph for Q.9 - 10 A 1.5 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the positive direction of x-axis is applied to the block. The force is given by F 4 x 2 ˆiN , where x is in metres and the initial position of the block is x = 0.

9. 10.

The maximum kinetic energy of the block between x = 0 and x = 2.0 m is : (A) 2.33 J (B) 8.67 J (C) 5.33 J

(D)

6.67 J

(D)

2

The maximum positive displacement x is : (A)

2 3

VMC/Energy & Momentum

(B)

2m

(C)

31

4m

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [3]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F x kx ax 3 . Here k and a are positive constants. For x 0 , the functional form of the potential energy U(x) of the particle is (see the figure) :

(A)

(B)

(C)

(D)

2.

A ladder 2.5 m long and of weight 150 N has its centre of mass 1 m from its bottom. A weight of 40 N is attached to the top end. The work required to raise the ladder from the horizontal position to the vertical position is : (A) 190 J (B) 250 J (C) 285 J (D) 475 J

3.

A body is moving up an inclined plane of angle with an initial kinetic energy E. The coefficient of friction between the plane and the body is . The work done against friction before the body comes to rest is : E cos E cos E cos (A) (B) (C) cos sin cos sin

4.

E cos cos sin

A mass M is lowered with the help of a string by a distance h at a constant acceleration g/2. The work done by the string will be : (A)

5.

(D)

Mgh 2

(B)

Mgh 2

(C)

3Mgh 2

(D)

3Mgh 2

In a certain situation, F and S are not equal to zero but the work done is zero. From this, we conclude that : (A) (B) F and S are in same direction F and S are in opposite direction (C) (D) F and S are at right angles F >S

6.

A ball is released from the top of a tower. The ratio of work done by force of gravity in 1st second, 2nd second and 3rd second of the motion of ball is : (A) 1:2:3 (B) 1 : 4 : 16 (C) 1:3:5 (D) 1 : 9 : 25

7.

A uniform chain of length L and mass M overhangs a horizontal table with two-third part on the table. The friction coefficient between the table and the chain is . The work done by the friction during the period the chain slips off the table is : 1 2 4 6 MgL MgL MgL MgL (A) (B) (C) (D) 4 9 9 7

8.

A spring of force constant 800 Nm 1 has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is : (A)

16 J

VMC/Energy & Momentum

(B)

8J

(C)

32

32 J

(D)

24 J

HWT/Physics

Vidyamandir Classes 9.

10.

If a particle is compelled to move on a given smooth plane curve under the action of given forces in the plane F xiˆ yjˆ , then :

1 2 F . dr mv 2

(A)

F . dr xdx ydy

(B)

(C)

F . dr xdx ydy

(D)

1 2 mv 2

xdx ydy

A 2.0 kg block is dropped from a height of 40 cm onto a spring of spring constant k 1960 Nm 1 . Find the maximum distance the spring is compressed. (A) 0.080 m

VMC/Energy & Momentum

(B)

0.20 m

(C)

33

0.40 m

(D)

0.10 m

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [4]

ROLL NO.

START TIME :

STUDENT’S SIGNATURE :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

An object of mass m is tied to a string of length L and a variable horizontal force is applied on it which starts at zero and gradually increases until the string makes an angle with the vertical. Work done by the force F is : (A)

mgL 1 sin

(B)

mgL

(C)

mgL 1 cos

(D)

mgL 1 cos

The kinetic energy K of a particle moving in straight line depends upon the distance s as : K as 2 The force acting on the particle is : (A)

3.

4:1

6.

(B)

2 :1

(C)

1:2

(B)

3E

(C)

5E

m1 m2 a b g

(B)

b m1m2 2 a m2 2 g

(C)

m1 b m2 a m2 g 2 2

(D)

m1 m2 a m1 2

(D)

as 2

(D)

1 : 16

(D)

7E

b g 2

What power must a sprinter, weighing 80 kg, develop from the start if he has to impart a velocity of 10 ms 1 to his body in 4s ? 1 kW

(B)

2 kW

(C)

3 kW

(D)

4 kW

(D)

r4 v

The power of a water jet flowing through an orifice of radius r with velocity v is : zero

(B)

r2 v2

(C)

r 2 v3

The power supplied by a force acting on a particle moving in a straight line is constant. The velocity of the particle varies with the displacement x as : (A)

9.

2a

(A)

(A) 8.

(C)

A rectangular plank of mass m1 and height a is kept on a horizontal surface. Another rectangular plank of mass m2 and height b is placed over the first plank. The gravitational potential energy of the system is :

(A) 7.

2 mas

The energy required to accelerate a car from rest to 10 ms 1 is E. What energy will be required to accelerate the car from 10 ms 1 to 20 ms 1 ? (A) E

5.

(B)

Two masses of 1g and 4g are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is : (A)

4.

2 as

x1 / 2

(B)

x

(C)

x2

(D)

x1 / 3

A gun of mass 20 kg has bullet of mass 0.1 kg in it. The gun is free to recoil and 804 J of recoil energy are released on firing the gun. The speed of bullet ( ms 1 ) is : (A)

10.

804 2010

(B)

10

(C)

40 10

(D)

804 2 103

The human heart discharges 75 cc of blood through the arteries at each bear against an average pressure of 10 cm of mercury. Assuming that the pulse frequency of 72 per minute the rate of working of heart in watt, is : (Density of mercury = 13.6 g/cc and

g 9.8 ms 2 ) (A)

11.9

VMC/Energy & Momentum

(B)

1.19

(C)

34

0.119

(D)

119

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [5]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, question marked with ‘*’ may have More than One correct option. 1.

A bullet when fired at a target with velocity of 100 ms 1 penetrates 1m into it. If the bullet is fired at a similar target with a thickness 0.5m, then it will emerge from it with a velocity of : 50 (A) (B) (C) m/s 50 2 m /s 2

2.

3.

50 m/s

(D)

10 m/s

A particle moves on a rough horizontal ground with some initial velocity v0. If 3/4th of its KE is lost in friction in time t0, the coefficient of friction between the particle and the ground is : v0 v0 3v0 v0 (A) (B) (C) (D) 2 gt0 4 gt0 4 gt0 gt0 A 0.5 kg ball is thrown up with an initial speed 14 ms 1 and reaches a maximum height of 8m. How much energy is dissipated by air drag acting on the ball during the ascent ? (A) 19.6 J (B) 4.9 J

(C)

10 J

(D)

9.8 J

Paragraph for Question 4 - 8 In a conservative force field, we can find the radial component of force F from the potential energy function (U) using the relation dU F . Positive values of F mean repulsive forces and vice-versa. We can find the equilibrium position, where force is zero. We can dr also calculate ionisation energy, which is the work done to move the particle from a certain position to infinity. Let us consider a particle bound to a certain point at a distance r from the centre of the force. The potential energy function of the particle is A B given by U r 2 , where A and B are positive constants. r r 4.

5.

*6.

The nature of equilibrium is : (A) Neutral (B)

The equilibrium distance (r0) of the particle is : 2A B (A) (B) B 2A If E (A)

7.

Stable

(C)

(C)

Unstable

A B

(D)

(D)

Cannot be predicted

B A

3B 2 represents total energy of particle and the motion is radial only, then velocity will be zero at : 16 A

r0

(B)

2 r0 3

(C)

2 r0 5

(D)

r0 3

(D)

4A B

The work required to move the particle from equilibrium position to infinity is : (A)

B2 4A

VMC/Energy & Momentum

(B)

4B 2 A

(C)

35

4B A

HWT/Physics

Vidyamandir Classes 8.

The nature of the force is : (A) attractive always (C) may be attractive or repulsive

(B) (D)

repulsive always cannot predict

9.

A constant power P is applied to a car starting from rest. If v is the velocity of the car at time t, then : 1 1 v (A) vt (B) (C) (D) v v t t t

10.

A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U (0) = 0, the graph of U (x) versus x will be, figure (where U is the potential energy function)

(A)

VMC/Energy & Momentum

(B)

(C)

36

(D)

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : E&M [6]

ROLL NO.

START TIME :

STUDENT’S SIGNATURE :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Which of the following graph depict the variation of kinetic energy of a ball bouncing on a horizontal floor with height ? (Neglect air resistance)

(A) 2.

3.

(B)

(C)

(D)

A uniform chain AB of mass m and length l is placed with one end A at the highest point of a hemisphere of radius R. Referring to R the top of the hemisphere as the datum level, the potential energy of the chain is : (Given that l ) 2 (A)

mR 2 g l l R sin R l

(B)

mR 2 g l l sin 2l R R

(C)

mR 2 g l l sin l R R

(D)

mR 2 g l l sin 2l R R

Two discs, each having mass m, are attached rigidly to the ends of a vertical spring. One of the discs rests on a horizontal surface and the other produces a compression x0 on the spring when it is in equilibrium. How much the spring to compressed so that when the force causing compression is removed, the extension of the spring will be able to lift the lower disc off the table : (A)

4.

5.

x0

(B)

2x0

Work done by static friction on an object : (A) may be positive (B) must be negative

(C)

3x0

(D)

1.5 x0

(C)

must be zero

(D)

None of these

(D)

Zero

A horse drinks water from a cubical container of side 1 m. The level of the stomach of horse is at 2m from the ground. Assume that all the water drunk by the horse is at a level of 2m 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 / s 2 ) (A)

10 J

VMC/Energy & Momentum

(B)

15 kJ

(C)

37

20 kJ

HWT/Physics

Vidyamandir Classes 6.

The given plot shows the variation of U, the potential energy of interaction between two particles, with the distance separating them, r I.

B and D are equilibrium points

II.

C is a point of stable equilibrium

III.

The force of interaction between the two particles is attractive between points C and B, and repulsive between points D and E on the curve

IV. The force of interaction between the particles is repulsive between points C and A. Which of the above statements are correct ? (A) 1 and 3 (B) 1 and 4 (C) 2 and 4 (D) 7.

8.

A uniform rope of linear mass density and length l is coiled on a smooth horizontal surface. One end is pulled up with constant velocity v. Then the average power applied by the external agent in pulling the entire rope just off the ground is : (A)

1 l 2 g lv 2 2 2

(B)

lg v

(C)

1 3 lvg v 2 2

(D)

lg v

(C)

If it is released at the origin, it will move in negative x-axis If it is released at x 2 where 0 , then its maximum speed will be 5 m/s and it will perform oscillatory motion If initially x 10 and u 6 ˆi , then it will cross x = 10

(D)

x 5 and x 5 are unstable equilibrium positions of the particle

A machine delivers power to a body which is proportional to velocity of the body. If the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to : (A)

10.

1 3 v 2

In the given figure the variation of potential energy of a particle of mass m = 2 kg is represented w.r.t. its x-coordinate. The particle moves under the effect of the conservative force along the x-axis. What of the following statements is incorrect about the particle.

(A) (B)

9.

2 and 3

V

(B)

V 2

(C)

v5 3

(D)

v2

From what minimum height h must the system be released when spring is unstretched so that after perfectly inelastic collision (e = 0) with ground, B may be lifted off the ground (spring constant = k) ? 4mg mg (A) (B) k 4k (C)

mg 2k

VMC/Energy & Momentum

(D)

None

38

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [7]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, question marked with ‘*’ may have More than One correct option. 1.

A light rigid rod of length L has a bob of mass M attached to one of its end just like a simple pendulum. Speed at the lowest point when it is inverted and released is : (A) (C)

2.

(B)

2gL

gL

(D)

5gL

A slab S of mass m is released from a height h0 from the top of a spring of force constant k. The maximum compression x of the spring is given by the equation : 1 1 mg h0 kx 2 mg h0 x kx 2 (A) (B) 2 2 (C)

3.

2

gL

mg h0

1 2 k h0 x 2

(D)

Under the action of a force, a 3 kg body moves such that x the force in first 3 second is : (A) 13.5 J (B)

27 J

mg h0 x

1 2 kx 2

t2 where position x is in meter and t is in second. The work done by 2

(C)

81 J

(D)

109 J

4.

A pogo stick essentially has a platform on a stiff coil spring. The natural length (uncompressed length) of the spring is 0.5 m long and spring constant of the spring is 1200 N/m. A person of mass 80 kg stands on the platform and compresses the spring by 0.1 m (so that he is about to be propelled into the air). At this instant, the gravitational potential energy of the person is (assume that the reference level for person’s gravitational PE is when the stands on ground without bending his legs) (A) To determine gravitational potential energy of the person in the given situation, location of centre of the gravity of the person must be known (B) 120 J (C) 400 J (D) 320 J

5.

The potential energy for a body of mass m that is acted on by a very massive body is given by v mgx

kx 2 . 3

The corresponding force is : (A) 6.

mg kx 2

(B)

mg kx 2

(C)

mg kx

(D)

mg kx

Two identical blocks, each having mass M, are placed as shown in the figure. These two blocks A and B are smoothly conjugated, so that when another block C of mass m passes from A to B there is no jerk. All the surfaces are frictionless and all three blocks are free to move. Block C is released from rest, then : (A) Block C will move for a very small duration (B) Block A will move for a very small duration (C) Block B will acquire maximum speed when C is at the lowest point on B and moving towards left (D) Block B will acquire maximum speed when C is at the topmost point of B

VMC/Energy & Momentum

39

HWT/Physics

Vidyamandir Classes 7.

An elastic string of unstretched length L and force constant k is stretched by a small length x. It is further stretched by another small length y. The work done in the second stretching is : 1 1 1 1 2 2 ky 2 x y k x y k x2 y2 ky (A) (B) (C) (D) 2 2 2 2

*8.

Consider the situation shown in the figure. The block of mass 1.0 kg is released from rest and it is found to have a speed of

0.3 ms 1 after it has descended through a distance of 1 m. Which of the following statements are correct ? (A) (B)

Loss in gravitational potential energy is 10 J Kinetic energy of 1 kg block is 0.045 J

(C)

4 kg block travels a distance of 2 m to acquire a velocity of 0.6 ms 1

(D)

Work done against friction is 80 J where is coefficient of kinetic friction

For Q.9 - 10 (A) (B) (C) (D)

Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1 Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for Statement-1 Statement-1 is True, Statement-2 is False Statement-1 is False, Statement-2 is True

9.

Statement 1 : In a circular motion, work done by centripetal force is not zero always. Statement 2 : If speed of the particle increases or decreases in circular motion, net force acting on the particle does not remain towards centre.

10.

Statement 1 : A small block of mass m is projected with some speed from point A on a smooth vertical tube track of small diameter as shown in the figure. The vertical heights of points B and C from point of projection are hB and hC hB = 2h and hC = h. The minimum possible speed of the block at point C is

2gh (where g is acceleration due to gravity)

Statement 2 : The minimum speed of the block at point C in situation given in statement 1 depends on hB hC .

VMC/Energy & Momentum

40

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [8]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

If W1, W2 and W3 represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 (as shown in figure) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W3. (A)

W1 W3 W2

(B)

W1 W2 W3

(C)

W1 W3 W2

(D)

W1 W2 W3

Paragraph for Q.2 - 3 A block of mass m is released from a height h1 along a smooth track as shown in the figure.

2.

Determine the force exerted on the block by the track at point 2, where radius of curvature is r1. (A)

3.

mg

m 2 gh1 r1

(B)

2mg

m 2 gh1 r1

(C)

mg m 2 gh1 2 r1

(D)

mg

m gh1 r1

Determine the minimum safe value of radius of curvature at point 3, so that the block does not fly off the track. (A)

h1 h2

(B)

2 h1 h2

(C)

h1 h2 3

(D)

2 h1 h2 3

Paragraph for Q.4 - 5 In the given figure, the mass m1 rests on a rough table. Now m1 is pushed against the spring by x to which it is not attached. Force constant of the spring is k and coefficient of friction is k .

4.

The speed of the blocks after the spring is released and has fallen a distance of h > x is : (A)

kx 2 2m2 gh 2 k m1 gh 2 m1 m2

(B)

kx 2 2m2 gh 2 k m1 gh m1 m2

(C)

kx 2 2m2 gh 2 k m1gh m1 m2

(D)

kx 2 2m2 gh 2 k m1gh 2 m1 m2

VMC/Energy & Momentum

41

HWT/Physics

Vidyamandir Classes 5.

If the spring is attached to the block where spring is initially at its original length and it falls a distance h' before coming to rest, the coefficient of friction k is :

1 kh 2 m1 g

m2 g (A)

1 kh 2 m1 g

m2 g (B)

1 kh 2 2m1 g

m2 g (C)

1 kh 2 2m1 g

m2 g (D)

Paragraph for Q.6 - 10 Ram and Ali are two fast friends since childhood. Ali neglected studies and now has no means to earn money other than a camel whereas Ram becomes an engineer. Now both are working in the same factory. Ali uses camel to transport the load within the factory. Due to low salary and degradation in health of camel, Ali becomes worried and meets his friend Ram and discusses his problems. Ram collected some data and with some assumption concluded the following. I.

The load used in each trip is 1000 kg and has friction coefficient k 0.1 and s 0.2 .

II.

Mass of camel is 500 kg.

III.

Load is accelerated for first 50 m with constant acceleration, then it is pulled at a constant speed of 5 m/s for 2 km and at last stopped with constant retardation in 50 m.

IV.

From biological data, the rate of consumption of energy of camel can be expressed as P 18 103 v 104 J / s where P is the power and v is the velocity of the camel. After calculations on different issues Ram suggested proper food, speed of camel, etc. to his friend. For the welfare of Ali, Ram wrote a letter to the management to increase his salary. (Assuming that the camel exerts a horizontal force on the load) :

6.

Sign of work done by the camel on the load during parts of motion : accelerated motion, uniform and retarded motion, respectively are : (A)

7.

(C)

+ve, zero –ve

(D)

+ve, zero, +ve

3:5

(B)

2.2 : 1

(C)

1:1

(D)

5:3

6250 J/s

(B)

5000 J/s

(C)

105 J/s

(D)

1250 J/s

The ratio of the work done by camel during uniform motion in the two cases when it moves with speed 5 m/s and when it moves with 10 m/s : (A)

10.

+ve, +ve, –ve

Maximum power transmitted by the camel to load is : (A)

9.

(B)

The ratio of magnitude of work done by camel on the load during accelerated motion to retarded motion is : (A)

8.

+ve, +ve, +ve

19/20

(B)

19/10

(C)

10/19

(D)

20/19

2.22 104 J

(D)

4.22 106 J

The total energy work done by camel during the trip of 2100 m is : (A)

2.1 106 J

VMC/Energy & Momentum

(B)

4.22 107 J

(C)

42

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [9]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Sand falls vertically at the rate of 5 kg/sec on a conveyor belt moving horizontally with a velocity of 0.6 m/sec. Find the extra force required to keep the belt moving (in N).

2.

The first ball of mass m moving with a velocity u collides head on with the second ball of mass m at rest. If the coefficient of restitution is e, then the ratio of the velocities of the first and the second ball after the collision is : (A)

1 e 1 e

(B)

1 e 1 e

(C)

1 e 2

(D)

1 e 2

3.

A billiard ball moving with a speed of 5 m/s collides with an identical ball, originally at rest. If the first ball stops dead after collision, then the second ball will move forward with a speed of : (A) 10 m/s (B) 5 m/s (C) 2.5 m/s (D) 1.0 m/s

4.

A particle of mass m is released from height ‘h’ on smooth quarter circular fixed wedge. The horizontal surface AB following the circular path at bottom of wedge is rough with coefficient of friction between surface and m. Find the distance from bottom of wedge where the mass will stop. 2h (A) (B) (C)

h g

(D)

h None of these

5.

A body just dropped from a tower explodes into two pieces of equal mass in mid-air. Which of the following is not possible ? (A) Each part will follow parabolic path (B) Only one part will follow parabolic path (C) Both parts move along a vertical line (D) One part reaches the ground earlier than the other

6.

A car of mass 400 kg travelling at 72 km/h crashes into a truck of mass 4000 kg travelling at 9 km/h in the same direction. The car bounces back at a speed of 18 km/h. The speed of the truck after the impact is : (A) 9 km/h (B) 18 km/h (C) 27 km/h (D) 36 km/h

7.

A ball of mass m collides horizontally with a stationary wedge on a rough horizontal surface, in the two orientations as shown. Neglect friction between the ball and the wedge. The students comment on the system of ball and wedge in these situations Saurav : Momentum of the system in x-direction will change by significant amount in both the cases. Rahul : There are no impulsive external forces in y-direction in both cases, hence the total momentum of the system in y-direction can be treated as conserved in both cases. (A) Saurav is wrong and Rahul is correct (B) Saurav is correct and Rahul is wrong (C) both the correct (D) both are wrong

VMC/Energy & Momentum

43

HWT/Physics

Vidyamandir Classes 8.

A plastic ball is dropped from a height of 1 m and rebounds several times from the floor. If 1.03 s elapse from the moment it is dropped to the second impact with the floor, what is the coefficient of restitution ? (A) 0.03 (B) 0.64 (C) 0.02 (D) 0.05

9.

A machinist starts with three identical square plates but cuts one corner from one of them, two corners from the second, and three corners from the third. Rank the three according to the x-coordinate of their centre of mass, from smallest to largest.

(A) 10.

3, 1, 2

(B)

1, 3, 2

(C)

3, 2, 1

(D)

1 and 3 tie, then 2

A block of mass M is tied to one end of a massless rope. The other end of the rope is in the hands of a man of mass 2M as shown. The block and the man are resting on a rough wedge of mass M. The whole system is resting on a smooth horizontal surface. The man starts walking towards right while holding the rope in his hands. Pulley is massless and frictionless. Find the displacement of the wedge when the block meets the pulley ? Assume wedge is sufficiently long so that man does not fall down. (A) 1/2 m towards right (B) 1/2 m towards left (C) The wedge does not move at all (D) 1 m towards left.

VMC/Energy & Momentum

44

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : E&M [10]

ROLL NO.

START TIME :

STUDENT’S SIGNATURE :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, question marked with ‘*’ may have More than One correct option. 1.

A train of mass M is moving on a circular track of radius ‘R’ with constant speed V. The length of the train is half of the perimeter of the track. The linear momentum of the train will be : 2MV (C) MVR Three balls A, B and C (mA = mC = 4mB) are placed on a smooth horizontal surface. Ball B collides with ball C with an initial velocity v as shown. Total number of collisions between the balls will be : (all collisions are elastic) (A) one (B) two (C) three

(A) 2.

0

(B)

(D)

MV

(D)

four

3.

A particle of mass m is made to move with uniform speed v0 along the perimeter of a regular hexagon, inscribed in a circle of radius R. The magnitude of impulse applied at each corner of the hexagon is : 2mv0 sin mv0 sin mv0 sin 2mv0 sin (A) (B) (C) (D) 6 6 3 3

4.

A stationary body explodes into two fragments of masses m1 and m2 . If momentum of one fragment is p, the energy of explosion is : (A)

*5.

6.

p2 2 m1 m2

(B)

p2 2 m1m2

(C)

p 2 m1 m2 2m1m2

(D)

p2 2 m1 m2

A pendulum bob of mass m connected to the end of an ideal string of length l is released from rest from horizontal position as shown. At the lowest point, the bob makes an elastic collision with a stationary block of mass 5m, which is kept on a frictionless surface. Mark out the correct statement(s) for the instant just after the impact. (A) Tension in the string 17 mg/9 (B) Tension in the string is 3 mg 2 gl 3 attained

(C)

The velocity of the block is

(D)

The

(B)

Statement-I is True, Statement-II is True and Statement-II is NOT a correct explanation for Statement-I.

(C) (D)

Statement-I is True, Statement-II is False. Statement-I is False, Statement-II is True.

maximum height by the pendulum bob after impact is (measured from the lowest 4l position) 9 In a long jump, it is possible to keep the top of your head moving at a constant height for a limited but finite Statement : I amount of time. By manipulating the vertical whereabouts of supple human body, the distance of the centre of mass Statement : II measured from the top of the head can be changed and this fact can be used to offset the deviation from a parabolic trajectory. (A) Statement-I is True, Statement-II is True and Statement-II is a correct explanation for Statement-I.

VMC/Energy & Momentum

45

HWT/Physics

Vidyamandir Classes 7.

Statement : I

In an elastic collision (e = 1) between two bodies, conservation of kinetic energy holds true, i.e., K1 K 2 i K1 K 2 f .

(A)

Conservation of momentum holds true, i.e., p1 p2 i p1 p2 i . Statement-I is True, Statement-II is True and Statement-II is a correct explanation for Statement-I.

(B)

Statement-I is True, Statement-II is True and Statement-II is NOT a correct explanation for Statement-I.

(C) (D)

Statement-I is True, Statement-II is False. Statement-I is False, Statement-II is True.

Statement : II

8.

Statement : I

A boy standing on a frictionless surface throws a ball. The body will move backwards.

Statement : II

In the absence of external force momentum will remain conserved.

(A)

Statement-I is True, Statement-II is True and Statement-II is a correct explanation for Statement-I.

(B)

Statement-I is True, Statement-II is True and Statement-II is NOT a correct explanation for Statement-I.

(C) (D)

Statement-I is True, Statement-II is False. Statement-I is False, Statement-II is True.

Paragraph for Q. 8 - 9 A ball mass m moving with velocity v strikes the bob of a pendulum at rest. The mass of the bob is also m. 9.

If the collision is perfectly inelastic, the height to which the bob will rise is given by : (A)

10.

v2 8g

(B)

v2 4g

(C)

v2 2g

(D)

v2 2g

2v 2 g

(D)

v2 g

If the collision is elastic, the height to which the bob will rise will be : (A)

v2 8g

VMC/Energy & Momentum

(B)

v2 2g

(C)

46

HWT/Physics

View more...
DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [1]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A raindrop of radius r falls from a certain height h above the ground. The work done by the gravitational force is proportional to : (A) r (B) r2 (C) r3 (D) r4

2.

When a spring is stretched by an amount x, the potential energy stored in it is V. When the same spring is stretched by an amount 2x, the potential energy stored in it will be : (A) V/2 (B) 2V (C) V/4 (D) 4V

3.

A pendulum has a length l. Its bob is pulled aside from its equilibrium position through an angle and then released. The speed of the bob when it passes through the equilibrium position is given by : (A)

2gl

(B)

2gl cos

(C)

2 gl 1 cos

(D)

2 gl 1 sin

4.

A moving bullet hits a solid target resting on a frictionless surface and gets embedded in it. What is conserved in this process ? (A) momentum and kinetic energy (B) kinetic energy alone (C) momentum alone (D) neither momentum nor kinetic energy

5.

Two identical balls marked 2 and 3, in contact with each other and at rest on a horizontal frictionless table, are hit head-one by another identical ball marked 1 moving initially with a speed v as shown in figure. What is observed, if the collision is elastic ?

(A) (B) (C) (D) 6.

The bob A of a pendulum released from a height h hits head-on another bob B of the same mass of an identical pendulum initially at rest. What is the result of this collision ? Assume the collision to be elastic (see figure).

(A) (B) (C) (D) 7.

Ball 1 comes to rest and balls 2 and 3 roll out with speed v/2 each Ball 1 and 2 come to rest and ball 3 roll out with speed v Balls 1, 2 and 3 roll out with speed v/3 each Balls 1, 2 and 3 come to rest

Bob A comes to rest at B and bob B moves to the left attaining a maximum height h Bobs A and B both move to the left, each attaining a maximum height h/2 Bob B moves to the left and bob A moves to the right, each attaining a maximum height h/2 Both bobs come to rest

A steel ball falls from a height h on a floor for which the coefficient of restitution is e. The height attained by the ball after two rebounds is : (A) eh (B) e2h (C) e3h (D) e4h

VMC/Energy & Momentum

28

HWT/Physics

Vidyamandir Classes 8.

For a head-on collision between two balls, velocities are exchanged if : (A) collision is elastic (B) balls have same radius (C) balls have same mass (D) both (A) and (C) together

9.

In figure, if M > m, the number of collisions between the balls will be :

(A) 10.

one

(B)

two

(C)

three

(D)

four

A body of mass m = 1 kg is dropped from a height h = 40 cm on a horizontal platform fixed to one end of an elastic spring, the other being fixed to a base. As a result the spring is compressed by an amount x = 10 cm. What is the force constant of the spring. Take = g 10 ms 2 . (A)

600 Nm 1

VMC/Energy & Momentum

(B)

800 Nm 1

(C)

29

1000 Nm 1

(D)

1200 Nm 1

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [2]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A body of mass 5 kg is moving along the x-axis with a velocity 2 ms 1 . Another body of mass 10 kg is moving along the y-axis with a velocity (A)

2.

3.

3ms 1 . They collide at the origin and stick together. The final velocity of the combined mass is :

3 ms 1

(B)

3 1 ms 1

(C)

4 1 ms 3

(D)

None

A spacecraft of mass M explodes into two parts when its velocity is V. After the explosion, one part of mass m is left stationary. What is the velocity of the other part ? MV MV MV mV (A) (B) (C) (D) m M m M m M m

A body of mass 2 kg moving with a velocity ˆi 2 ˆj 3kˆ ms 1 collides with another body of mass 3 kg moving with a velocity

2ˆi ˆj kˆ in ms . If they stick together, the velocity in ms 1 ˆ (A) 8i 7 ˆj 3kˆ (B) 15 4ˆi ˆj 3kˆ (C) 5 1

1

of the composite body is :

1 ˆ ˆ ˆ 8i j k 5

(D)

1 4ˆi 7 ˆj 3kˆ 5

4.

Two equal spheres A and B lie on a smooth horizontal circular groove at opposite ends of a diameter. Sphere A is projected along the groove and at the end of time T impinges on sphere B. If e is the coefficient of restitution, the second impact will occur after a time equal to : 2T (A) T (B) eT (C) (D) 2eT e

5.

Two masses M and m (with M > m) are connected by means of a pulley as shown in figure. The system is released. At the instant when mass M has fallen through a distance h, the velocity of mass m will be : (A)

(C)

2gh

2gh M m

M m

VMC/Energy & Momentum

(B)

(D)

2gh M m

2gh M m

M m

30

HWT/Physics

Vidyamandir Classes 6.

A mass m, lying on a horizontal frictionless surface is connected to mass M as shown in figure. The system is now released. The velocity of mass m when mass M is descended a distance h is : (A) (C)

7.

2Mgh

M m

(B)

2mgh M

(D)

2gh

A uniform rope of length L is lying in a lump on a frictionless table. A small part of the rope is held hanging through a hole in the table just below the lump. The system is then released. The speed of the end of the rope as it leaves the hole is : (A)

8.

2Mgh m

(B)

gL

2

gL 3

(C)

2 gL 3

(D)

zero

A bullet of mass m is fired horizontally with a velocity v on a wooden block of mass M suspended from a support and gets embedded in it. The kinetic energy of the bullet + block system is : (A)

1 2 mv 2

1 M m v2 2

(B)

(C)

Mmv 2 2 M m

(D)

m2v 2 2 M m

Paragraph for Q.9 - 10 A 1.5 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the positive direction of x-axis is applied to the block. The force is given by F 4 x 2 ˆiN , where x is in metres and the initial position of the block is x = 0.

9. 10.

The maximum kinetic energy of the block between x = 0 and x = 2.0 m is : (A) 2.33 J (B) 8.67 J (C) 5.33 J

(D)

6.67 J

(D)

2

The maximum positive displacement x is : (A)

2 3

VMC/Energy & Momentum

(B)

2m

(C)

31

4m

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [3]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F x kx ax 3 . Here k and a are positive constants. For x 0 , the functional form of the potential energy U(x) of the particle is (see the figure) :

(A)

(B)

(C)

(D)

2.

A ladder 2.5 m long and of weight 150 N has its centre of mass 1 m from its bottom. A weight of 40 N is attached to the top end. The work required to raise the ladder from the horizontal position to the vertical position is : (A) 190 J (B) 250 J (C) 285 J (D) 475 J

3.

A body is moving up an inclined plane of angle with an initial kinetic energy E. The coefficient of friction between the plane and the body is . The work done against friction before the body comes to rest is : E cos E cos E cos (A) (B) (C) cos sin cos sin

4.

E cos cos sin

A mass M is lowered with the help of a string by a distance h at a constant acceleration g/2. The work done by the string will be : (A)

5.

(D)

Mgh 2

(B)

Mgh 2

(C)

3Mgh 2

(D)

3Mgh 2

In a certain situation, F and S are not equal to zero but the work done is zero. From this, we conclude that : (A) (B) F and S are in same direction F and S are in opposite direction (C) (D) F and S are at right angles F >S

6.

A ball is released from the top of a tower. The ratio of work done by force of gravity in 1st second, 2nd second and 3rd second of the motion of ball is : (A) 1:2:3 (B) 1 : 4 : 16 (C) 1:3:5 (D) 1 : 9 : 25

7.

A uniform chain of length L and mass M overhangs a horizontal table with two-third part on the table. The friction coefficient between the table and the chain is . The work done by the friction during the period the chain slips off the table is : 1 2 4 6 MgL MgL MgL MgL (A) (B) (C) (D) 4 9 9 7

8.

A spring of force constant 800 Nm 1 has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is : (A)

16 J

VMC/Energy & Momentum

(B)

8J

(C)

32

32 J

(D)

24 J

HWT/Physics

Vidyamandir Classes 9.

10.

If a particle is compelled to move on a given smooth plane curve under the action of given forces in the plane F xiˆ yjˆ , then :

1 2 F . dr mv 2

(A)

F . dr xdx ydy

(B)

(C)

F . dr xdx ydy

(D)

1 2 mv 2

xdx ydy

A 2.0 kg block is dropped from a height of 40 cm onto a spring of spring constant k 1960 Nm 1 . Find the maximum distance the spring is compressed. (A) 0.080 m

VMC/Energy & Momentum

(B)

0.20 m

(C)

33

0.40 m

(D)

0.10 m

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [4]

ROLL NO.

START TIME :

STUDENT’S SIGNATURE :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

An object of mass m is tied to a string of length L and a variable horizontal force is applied on it which starts at zero and gradually increases until the string makes an angle with the vertical. Work done by the force F is : (A)

mgL 1 sin

(B)

mgL

(C)

mgL 1 cos

(D)

mgL 1 cos

The kinetic energy K of a particle moving in straight line depends upon the distance s as : K as 2 The force acting on the particle is : (A)

3.

4:1

6.

(B)

2 :1

(C)

1:2

(B)

3E

(C)

5E

m1 m2 a b g

(B)

b m1m2 2 a m2 2 g

(C)

m1 b m2 a m2 g 2 2

(D)

m1 m2 a m1 2

(D)

as 2

(D)

1 : 16

(D)

7E

b g 2

What power must a sprinter, weighing 80 kg, develop from the start if he has to impart a velocity of 10 ms 1 to his body in 4s ? 1 kW

(B)

2 kW

(C)

3 kW

(D)

4 kW

(D)

r4 v

The power of a water jet flowing through an orifice of radius r with velocity v is : zero

(B)

r2 v2

(C)

r 2 v3

The power supplied by a force acting on a particle moving in a straight line is constant. The velocity of the particle varies with the displacement x as : (A)

9.

2a

(A)

(A) 8.

(C)

A rectangular plank of mass m1 and height a is kept on a horizontal surface. Another rectangular plank of mass m2 and height b is placed over the first plank. The gravitational potential energy of the system is :

(A) 7.

2 mas

The energy required to accelerate a car from rest to 10 ms 1 is E. What energy will be required to accelerate the car from 10 ms 1 to 20 ms 1 ? (A) E

5.

(B)

Two masses of 1g and 4g are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is : (A)

4.

2 as

x1 / 2

(B)

x

(C)

x2

(D)

x1 / 3

A gun of mass 20 kg has bullet of mass 0.1 kg in it. The gun is free to recoil and 804 J of recoil energy are released on firing the gun. The speed of bullet ( ms 1 ) is : (A)

10.

804 2010

(B)

10

(C)

40 10

(D)

804 2 103

The human heart discharges 75 cc of blood through the arteries at each bear against an average pressure of 10 cm of mercury. Assuming that the pulse frequency of 72 per minute the rate of working of heart in watt, is : (Density of mercury = 13.6 g/cc and

g 9.8 ms 2 ) (A)

11.9

VMC/Energy & Momentum

(B)

1.19

(C)

34

0.119

(D)

119

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [5]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, question marked with ‘*’ may have More than One correct option. 1.

A bullet when fired at a target with velocity of 100 ms 1 penetrates 1m into it. If the bullet is fired at a similar target with a thickness 0.5m, then it will emerge from it with a velocity of : 50 (A) (B) (C) m/s 50 2 m /s 2

2.

3.

50 m/s

(D)

10 m/s

A particle moves on a rough horizontal ground with some initial velocity v0. If 3/4th of its KE is lost in friction in time t0, the coefficient of friction between the particle and the ground is : v0 v0 3v0 v0 (A) (B) (C) (D) 2 gt0 4 gt0 4 gt0 gt0 A 0.5 kg ball is thrown up with an initial speed 14 ms 1 and reaches a maximum height of 8m. How much energy is dissipated by air drag acting on the ball during the ascent ? (A) 19.6 J (B) 4.9 J

(C)

10 J

(D)

9.8 J

Paragraph for Question 4 - 8 In a conservative force field, we can find the radial component of force F from the potential energy function (U) using the relation dU F . Positive values of F mean repulsive forces and vice-versa. We can find the equilibrium position, where force is zero. We can dr also calculate ionisation energy, which is the work done to move the particle from a certain position to infinity. Let us consider a particle bound to a certain point at a distance r from the centre of the force. The potential energy function of the particle is A B given by U r 2 , where A and B are positive constants. r r 4.

5.

*6.

The nature of equilibrium is : (A) Neutral (B)

The equilibrium distance (r0) of the particle is : 2A B (A) (B) B 2A If E (A)

7.

Stable

(C)

(C)

Unstable

A B

(D)

(D)

Cannot be predicted

B A

3B 2 represents total energy of particle and the motion is radial only, then velocity will be zero at : 16 A

r0

(B)

2 r0 3

(C)

2 r0 5

(D)

r0 3

(D)

4A B

The work required to move the particle from equilibrium position to infinity is : (A)

B2 4A

VMC/Energy & Momentum

(B)

4B 2 A

(C)

35

4B A

HWT/Physics

Vidyamandir Classes 8.

The nature of the force is : (A) attractive always (C) may be attractive or repulsive

(B) (D)

repulsive always cannot predict

9.

A constant power P is applied to a car starting from rest. If v is the velocity of the car at time t, then : 1 1 v (A) vt (B) (C) (D) v v t t t

10.

A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U (0) = 0, the graph of U (x) versus x will be, figure (where U is the potential energy function)

(A)

VMC/Energy & Momentum

(B)

(C)

36

(D)

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : E&M [6]

ROLL NO.

START TIME :

STUDENT’S SIGNATURE :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Which of the following graph depict the variation of kinetic energy of a ball bouncing on a horizontal floor with height ? (Neglect air resistance)

(A) 2.

3.

(B)

(C)

(D)

A uniform chain AB of mass m and length l is placed with one end A at the highest point of a hemisphere of radius R. Referring to R the top of the hemisphere as the datum level, the potential energy of the chain is : (Given that l ) 2 (A)

mR 2 g l l R sin R l

(B)

mR 2 g l l sin 2l R R

(C)

mR 2 g l l sin l R R

(D)

mR 2 g l l sin 2l R R

Two discs, each having mass m, are attached rigidly to the ends of a vertical spring. One of the discs rests on a horizontal surface and the other produces a compression x0 on the spring when it is in equilibrium. How much the spring to compressed so that when the force causing compression is removed, the extension of the spring will be able to lift the lower disc off the table : (A)

4.

5.

x0

(B)

2x0

Work done by static friction on an object : (A) may be positive (B) must be negative

(C)

3x0

(D)

1.5 x0

(C)

must be zero

(D)

None of these

(D)

Zero

A horse drinks water from a cubical container of side 1 m. The level of the stomach of horse is at 2m from the ground. Assume that all the water drunk by the horse is at a level of 2m 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 / s 2 ) (A)

10 J

VMC/Energy & Momentum

(B)

15 kJ

(C)

37

20 kJ

HWT/Physics

Vidyamandir Classes 6.

The given plot shows the variation of U, the potential energy of interaction between two particles, with the distance separating them, r I.

B and D are equilibrium points

II.

C is a point of stable equilibrium

III.

The force of interaction between the two particles is attractive between points C and B, and repulsive between points D and E on the curve

IV. The force of interaction between the particles is repulsive between points C and A. Which of the above statements are correct ? (A) 1 and 3 (B) 1 and 4 (C) 2 and 4 (D) 7.

8.

A uniform rope of linear mass density and length l is coiled on a smooth horizontal surface. One end is pulled up with constant velocity v. Then the average power applied by the external agent in pulling the entire rope just off the ground is : (A)

1 l 2 g lv 2 2 2

(B)

lg v

(C)

1 3 lvg v 2 2

(D)

lg v

(C)

If it is released at the origin, it will move in negative x-axis If it is released at x 2 where 0 , then its maximum speed will be 5 m/s and it will perform oscillatory motion If initially x 10 and u 6 ˆi , then it will cross x = 10

(D)

x 5 and x 5 are unstable equilibrium positions of the particle

A machine delivers power to a body which is proportional to velocity of the body. If the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to : (A)

10.

1 3 v 2

In the given figure the variation of potential energy of a particle of mass m = 2 kg is represented w.r.t. its x-coordinate. The particle moves under the effect of the conservative force along the x-axis. What of the following statements is incorrect about the particle.

(A) (B)

9.

2 and 3

V

(B)

V 2

(C)

v5 3

(D)

v2

From what minimum height h must the system be released when spring is unstretched so that after perfectly inelastic collision (e = 0) with ground, B may be lifted off the ground (spring constant = k) ? 4mg mg (A) (B) k 4k (C)

mg 2k

VMC/Energy & Momentum

(D)

None

38

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [7]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, question marked with ‘*’ may have More than One correct option. 1.

A light rigid rod of length L has a bob of mass M attached to one of its end just like a simple pendulum. Speed at the lowest point when it is inverted and released is : (A) (C)

2.

(B)

2gL

gL

(D)

5gL

A slab S of mass m is released from a height h0 from the top of a spring of force constant k. The maximum compression x of the spring is given by the equation : 1 1 mg h0 kx 2 mg h0 x kx 2 (A) (B) 2 2 (C)

3.

2

gL

mg h0

1 2 k h0 x 2

(D)

Under the action of a force, a 3 kg body moves such that x the force in first 3 second is : (A) 13.5 J (B)

27 J

mg h0 x

1 2 kx 2

t2 where position x is in meter and t is in second. The work done by 2

(C)

81 J

(D)

109 J

4.

A pogo stick essentially has a platform on a stiff coil spring. The natural length (uncompressed length) of the spring is 0.5 m long and spring constant of the spring is 1200 N/m. A person of mass 80 kg stands on the platform and compresses the spring by 0.1 m (so that he is about to be propelled into the air). At this instant, the gravitational potential energy of the person is (assume that the reference level for person’s gravitational PE is when the stands on ground without bending his legs) (A) To determine gravitational potential energy of the person in the given situation, location of centre of the gravity of the person must be known (B) 120 J (C) 400 J (D) 320 J

5.

The potential energy for a body of mass m that is acted on by a very massive body is given by v mgx

kx 2 . 3

The corresponding force is : (A) 6.

mg kx 2

(B)

mg kx 2

(C)

mg kx

(D)

mg kx

Two identical blocks, each having mass M, are placed as shown in the figure. These two blocks A and B are smoothly conjugated, so that when another block C of mass m passes from A to B there is no jerk. All the surfaces are frictionless and all three blocks are free to move. Block C is released from rest, then : (A) Block C will move for a very small duration (B) Block A will move for a very small duration (C) Block B will acquire maximum speed when C is at the lowest point on B and moving towards left (D) Block B will acquire maximum speed when C is at the topmost point of B

VMC/Energy & Momentum

39

HWT/Physics

Vidyamandir Classes 7.

An elastic string of unstretched length L and force constant k is stretched by a small length x. It is further stretched by another small length y. The work done in the second stretching is : 1 1 1 1 2 2 ky 2 x y k x y k x2 y2 ky (A) (B) (C) (D) 2 2 2 2

*8.

Consider the situation shown in the figure. The block of mass 1.0 kg is released from rest and it is found to have a speed of

0.3 ms 1 after it has descended through a distance of 1 m. Which of the following statements are correct ? (A) (B)

Loss in gravitational potential energy is 10 J Kinetic energy of 1 kg block is 0.045 J

(C)

4 kg block travels a distance of 2 m to acquire a velocity of 0.6 ms 1

(D)

Work done against friction is 80 J where is coefficient of kinetic friction

For Q.9 - 10 (A) (B) (C) (D)

Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1 Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for Statement-1 Statement-1 is True, Statement-2 is False Statement-1 is False, Statement-2 is True

9.

Statement 1 : In a circular motion, work done by centripetal force is not zero always. Statement 2 : If speed of the particle increases or decreases in circular motion, net force acting on the particle does not remain towards centre.

10.

Statement 1 : A small block of mass m is projected with some speed from point A on a smooth vertical tube track of small diameter as shown in the figure. The vertical heights of points B and C from point of projection are hB and hC hB = 2h and hC = h. The minimum possible speed of the block at point C is

2gh (where g is acceleration due to gravity)

Statement 2 : The minimum speed of the block at point C in situation given in statement 1 depends on hB hC .

VMC/Energy & Momentum

40

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [8]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

If W1, W2 and W3 represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 (as shown in figure) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W3. (A)

W1 W3 W2

(B)

W1 W2 W3

(C)

W1 W3 W2

(D)

W1 W2 W3

Paragraph for Q.2 - 3 A block of mass m is released from a height h1 along a smooth track as shown in the figure.

2.

Determine the force exerted on the block by the track at point 2, where radius of curvature is r1. (A)

3.

mg

m 2 gh1 r1

(B)

2mg

m 2 gh1 r1

(C)

mg m 2 gh1 2 r1

(D)

mg

m gh1 r1

Determine the minimum safe value of radius of curvature at point 3, so that the block does not fly off the track. (A)

h1 h2

(B)

2 h1 h2

(C)

h1 h2 3

(D)

2 h1 h2 3

Paragraph for Q.4 - 5 In the given figure, the mass m1 rests on a rough table. Now m1 is pushed against the spring by x to which it is not attached. Force constant of the spring is k and coefficient of friction is k .

4.

The speed of the blocks after the spring is released and has fallen a distance of h > x is : (A)

kx 2 2m2 gh 2 k m1 gh 2 m1 m2

(B)

kx 2 2m2 gh 2 k m1 gh m1 m2

(C)

kx 2 2m2 gh 2 k m1gh m1 m2

(D)

kx 2 2m2 gh 2 k m1gh 2 m1 m2

VMC/Energy & Momentum

41

HWT/Physics

Vidyamandir Classes 5.

If the spring is attached to the block where spring is initially at its original length and it falls a distance h' before coming to rest, the coefficient of friction k is :

1 kh 2 m1 g

m2 g (A)

1 kh 2 m1 g

m2 g (B)

1 kh 2 2m1 g

m2 g (C)

1 kh 2 2m1 g

m2 g (D)

Paragraph for Q.6 - 10 Ram and Ali are two fast friends since childhood. Ali neglected studies and now has no means to earn money other than a camel whereas Ram becomes an engineer. Now both are working in the same factory. Ali uses camel to transport the load within the factory. Due to low salary and degradation in health of camel, Ali becomes worried and meets his friend Ram and discusses his problems. Ram collected some data and with some assumption concluded the following. I.

The load used in each trip is 1000 kg and has friction coefficient k 0.1 and s 0.2 .

II.

Mass of camel is 500 kg.

III.

Load is accelerated for first 50 m with constant acceleration, then it is pulled at a constant speed of 5 m/s for 2 km and at last stopped with constant retardation in 50 m.

IV.

From biological data, the rate of consumption of energy of camel can be expressed as P 18 103 v 104 J / s where P is the power and v is the velocity of the camel. After calculations on different issues Ram suggested proper food, speed of camel, etc. to his friend. For the welfare of Ali, Ram wrote a letter to the management to increase his salary. (Assuming that the camel exerts a horizontal force on the load) :

6.

Sign of work done by the camel on the load during parts of motion : accelerated motion, uniform and retarded motion, respectively are : (A)

7.

(C)

+ve, zero –ve

(D)

+ve, zero, +ve

3:5

(B)

2.2 : 1

(C)

1:1

(D)

5:3

6250 J/s

(B)

5000 J/s

(C)

105 J/s

(D)

1250 J/s

The ratio of the work done by camel during uniform motion in the two cases when it moves with speed 5 m/s and when it moves with 10 m/s : (A)

10.

+ve, +ve, –ve

Maximum power transmitted by the camel to load is : (A)

9.

(B)

The ratio of magnitude of work done by camel on the load during accelerated motion to retarded motion is : (A)

8.

+ve, +ve, +ve

19/20

(B)

19/10

(C)

10/19

(D)

20/19

2.22 104 J

(D)

4.22 106 J

The total energy work done by camel during the trip of 2100 m is : (A)

2.1 106 J

VMC/Energy & Momentum

(B)

4.22 107 J

(C)

42

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : E&M [9]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Sand falls vertically at the rate of 5 kg/sec on a conveyor belt moving horizontally with a velocity of 0.6 m/sec. Find the extra force required to keep the belt moving (in N).

2.

The first ball of mass m moving with a velocity u collides head on with the second ball of mass m at rest. If the coefficient of restitution is e, then the ratio of the velocities of the first and the second ball after the collision is : (A)

1 e 1 e

(B)

1 e 1 e

(C)

1 e 2

(D)

1 e 2

3.

A billiard ball moving with a speed of 5 m/s collides with an identical ball, originally at rest. If the first ball stops dead after collision, then the second ball will move forward with a speed of : (A) 10 m/s (B) 5 m/s (C) 2.5 m/s (D) 1.0 m/s

4.

A particle of mass m is released from height ‘h’ on smooth quarter circular fixed wedge. The horizontal surface AB following the circular path at bottom of wedge is rough with coefficient of friction between surface and m. Find the distance from bottom of wedge where the mass will stop. 2h (A) (B) (C)

h g

(D)

h None of these

5.

A body just dropped from a tower explodes into two pieces of equal mass in mid-air. Which of the following is not possible ? (A) Each part will follow parabolic path (B) Only one part will follow parabolic path (C) Both parts move along a vertical line (D) One part reaches the ground earlier than the other

6.

A car of mass 400 kg travelling at 72 km/h crashes into a truck of mass 4000 kg travelling at 9 km/h in the same direction. The car bounces back at a speed of 18 km/h. The speed of the truck after the impact is : (A) 9 km/h (B) 18 km/h (C) 27 km/h (D) 36 km/h

7.

A ball of mass m collides horizontally with a stationary wedge on a rough horizontal surface, in the two orientations as shown. Neglect friction between the ball and the wedge. The students comment on the system of ball and wedge in these situations Saurav : Momentum of the system in x-direction will change by significant amount in both the cases. Rahul : There are no impulsive external forces in y-direction in both cases, hence the total momentum of the system in y-direction can be treated as conserved in both cases. (A) Saurav is wrong and Rahul is correct (B) Saurav is correct and Rahul is wrong (C) both the correct (D) both are wrong

VMC/Energy & Momentum

43

HWT/Physics

Vidyamandir Classes 8.

A plastic ball is dropped from a height of 1 m and rebounds several times from the floor. If 1.03 s elapse from the moment it is dropped to the second impact with the floor, what is the coefficient of restitution ? (A) 0.03 (B) 0.64 (C) 0.02 (D) 0.05

9.

A machinist starts with three identical square plates but cuts one corner from one of them, two corners from the second, and three corners from the third. Rank the three according to the x-coordinate of their centre of mass, from smallest to largest.

(A) 10.

3, 1, 2

(B)

1, 3, 2

(C)

3, 2, 1

(D)

1 and 3 tie, then 2

A block of mass M is tied to one end of a massless rope. The other end of the rope is in the hands of a man of mass 2M as shown. The block and the man are resting on a rough wedge of mass M. The whole system is resting on a smooth horizontal surface. The man starts walking towards right while holding the rope in his hands. Pulley is massless and frictionless. Find the displacement of the wedge when the block meets the pulley ? Assume wedge is sufficiently long so that man does not fall down. (A) 1/2 m towards right (B) 1/2 m towards left (C) The wedge does not move at all (D) 1 m towards left.

VMC/Energy & Momentum

44

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : E&M [10]

ROLL NO.

START TIME :

STUDENT’S SIGNATURE :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, question marked with ‘*’ may have More than One correct option. 1.

A train of mass M is moving on a circular track of radius ‘R’ with constant speed V. The length of the train is half of the perimeter of the track. The linear momentum of the train will be : 2MV (C) MVR Three balls A, B and C (mA = mC = 4mB) are placed on a smooth horizontal surface. Ball B collides with ball C with an initial velocity v as shown. Total number of collisions between the balls will be : (all collisions are elastic) (A) one (B) two (C) three

(A) 2.

0

(B)

(D)

MV

(D)

four

3.

A particle of mass m is made to move with uniform speed v0 along the perimeter of a regular hexagon, inscribed in a circle of radius R. The magnitude of impulse applied at each corner of the hexagon is : 2mv0 sin mv0 sin mv0 sin 2mv0 sin (A) (B) (C) (D) 6 6 3 3

4.

A stationary body explodes into two fragments of masses m1 and m2 . If momentum of one fragment is p, the energy of explosion is : (A)

*5.

6.

p2 2 m1 m2

(B)

p2 2 m1m2

(C)

p 2 m1 m2 2m1m2

(D)

p2 2 m1 m2

A pendulum bob of mass m connected to the end of an ideal string of length l is released from rest from horizontal position as shown. At the lowest point, the bob makes an elastic collision with a stationary block of mass 5m, which is kept on a frictionless surface. Mark out the correct statement(s) for the instant just after the impact. (A) Tension in the string 17 mg/9 (B) Tension in the string is 3 mg 2 gl 3 attained

(C)

The velocity of the block is

(D)

The

(B)

Statement-I is True, Statement-II is True and Statement-II is NOT a correct explanation for Statement-I.

(C) (D)

Statement-I is True, Statement-II is False. Statement-I is False, Statement-II is True.

maximum height by the pendulum bob after impact is (measured from the lowest 4l position) 9 In a long jump, it is possible to keep the top of your head moving at a constant height for a limited but finite Statement : I amount of time. By manipulating the vertical whereabouts of supple human body, the distance of the centre of mass Statement : II measured from the top of the head can be changed and this fact can be used to offset the deviation from a parabolic trajectory. (A) Statement-I is True, Statement-II is True and Statement-II is a correct explanation for Statement-I.

VMC/Energy & Momentum

45

HWT/Physics

Vidyamandir Classes 7.

Statement : I

In an elastic collision (e = 1) between two bodies, conservation of kinetic energy holds true, i.e., K1 K 2 i K1 K 2 f .

(A)

Conservation of momentum holds true, i.e., p1 p2 i p1 p2 i . Statement-I is True, Statement-II is True and Statement-II is a correct explanation for Statement-I.

(B)

Statement-I is True, Statement-II is True and Statement-II is NOT a correct explanation for Statement-I.

(C) (D)

Statement-I is True, Statement-II is False. Statement-I is False, Statement-II is True.

Statement : II

8.

Statement : I

A boy standing on a frictionless surface throws a ball. The body will move backwards.

Statement : II

In the absence of external force momentum will remain conserved.

(A)

Statement-I is True, Statement-II is True and Statement-II is a correct explanation for Statement-I.

(B)

Statement-I is True, Statement-II is True and Statement-II is NOT a correct explanation for Statement-I.

(C) (D)

Statement-I is True, Statement-II is False. Statement-I is False, Statement-II is True.

Paragraph for Q. 8 - 9 A ball mass m moving with velocity v strikes the bob of a pendulum at rest. The mass of the bob is also m. 9.

If the collision is perfectly inelastic, the height to which the bob will rise is given by : (A)

10.

v2 8g

(B)

v2 4g

(C)

v2 2g

(D)

v2 2g

2v 2 g

(D)

v2 g

If the collision is elastic, the height to which the bob will rise will be : (A)

v2 8g

VMC/Energy & Momentum

(B)

v2 2g

(C)

46

HWT/Physics

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