Physics galaxy mechanics worksheet

PG Brainstormer - 1H

PG Brain Stormer - 1 H RECTILINEAR MOTION, PROJECTILE MOTION/2D MOTION, RELATIVE MOTION

An Ultimate Tool to understand advanced High School Physics by ASHISH ARORA Sir

Time Allowed

90 Min

Maximum Marks

110

Instruction : In Section A each question is of 3 Marks and there is a negative marking of -1 Mark whereas in Section B there is no negative marking and each question is of 5 Marks

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Section - A Single Choice Correct (Q. No. 1 to 20) The Questions given in this section are MCQs with four answer options (A), (B), (C) and (D) out of which ONLY ONE is correct. Choose the correct answer and fill the answer in the OMR sheet provided at the end. 1.

Two cars are moving in the same direction with a speed of 30 km h–1. They are separated from each other by 5 km. Third car moving in the opposite direction meets the two cars after an interval of 4 minutes. What is the speed of the third car ? (A) 30 km h–1 (B) 35 km h–1 (C) 40 km h–1 (D*) 45 km h–1

2.

Ship A is moving with velocity 30 m/s due east and ship B with velocity 40 m/s due north. Initial separation between the ships is 10 km as shown in figure. After what time ships are closest to each other : 40 m/s (A) 80 sec (B*) 120 sec 30 m/s (C) 160 sec (D) None B A 10 km

A steam boat goes across a lake and comes back (i) on a quiet day when the water is still and (ii) on a rough day when there is a uniform current so as to help the journey onwards and to impede the journey back. If the speed of the launch on both days was same, the time required for complete journey on the rough day, as compared to the quiet day will be : (A*) More (B) Less (C) Same (D) None of these

4.

A car with a vertical wind shield moves along in a rain storm at speed of 40 km h–1. The rain drops fall vertically with a terminal speed of 20 m s–1. The angle at which the rain drops strike the wind shield is : (A) tan–1 (2/3) (B) tan–1 (3/2) (C*) tan–1 (5/9) (D) tan–1 (9/5)

5.

A smooth square horizontal platform ABCD is moving towards right with a uniform speed v. At what angle  must a particle be projected from A with speed u so that it strikes the point B :

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3.

u   v

u (C) cos–1   v

(A)

7.

–1

(B*) cos

C

v   u

u

v



v (D) sin–1   u

A

D

Three particles start from the origin at the same time, one with a velocity v1 along x-axis, the second along the y-axis with a velocity v2 and the third along x = y line. The velocity of the third so that the three may always lie on the same line is :

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6.

B

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(A) sin

–1

v1v 2 v1  v 2

(B*)

2 v1v 2 v1  v 2

(C)

3v1v 2 v1  v2

(D) zero

A motorboat going down stream overcame a raft at a point A. 60 minute later it turned back and after some time passed the raft at a distance of 6 km from the point A. Assuming the duty of the engine to be constant, the flow velocity is : (A*) 3 kmh–1 (B) 4 kmh–1 (C) 5 kmh–1 (D) 6 kmh–1

8.

PG Brainstormer - 1H The velocity of a boat in still water is  times less than the velocity of flow of the river ( > 1). The angle with the stream direction at which the boat must move to minimum drifting is : 1 (A) sin–1    

1 (B) cot–1    

(C*)

 + sin–1 2

1    

(D)

 + cot–1 2

1    

Two points, A and B, are located on the ground at a certain distance d apart. Two stones are launched simultaneously from points A and B with equal speeds but at different angles. Each stone lands at the launch point of the other. Knowing that one of the stone is launched at an angle > 45o with the horizontal. Then the minimum distance between the stones during the flight will be : (A) d sin (B*) d sin( – 45º) (C) d cos( – 45º) (D) d cos 

10.

At the initial moment three points A, B, and C are on a horizontal straight line at equal distances from one another. Point A begins to move vertically upward with constant velocity v and point C vertically downward without any initial velocity at constant acceleration a. Assuming the points begin to move simultaneously, then for all the points to be constantly on one straight line the point B move with : (A) acceleration

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9.

1 1 a and initial velocity v both upward 2 2

1 1 a and initial velocity v both upward 2 2 (C) zero acceleration and initial velocity v

(B*) retardation

(D) acceleration 11.

1 a and initial velocity v both downward 2

A swimmer crosses a river in minimum possible time of 10 second. And when he reaches the other end, he starts swimming in a direction towards the point from where he initially started swimming. Keeping the direction of his velocity relative to river current fixed, the swimmer crosses the river in 15 sec. The ratio of speed of swimmer with respect to water and the speed of river flow is (Assume constant speed of river & swimmer) : (A)

3 2

(B)

9 4

(C*)

2 5

(D)

5 2

Wind is blowing at a harbour with a speed of 72 kmh –1 and the flag on the mast of a boat anchored at harbour flutters along the North-East direction. If the boat starts moving at a speed of 51 kmh –1 due North, the direction of the flag is (in approximation) : (A*) towards east (B) towards west (C) towards north (D) towards south

13.

A particle is thrown up inside a stationary lift of sufficient height. The time of flight is T. Now it is thrown again with same initial speed 0 with respect to lift. At the time of second throw, lift is moving up with speed 0 and uniform acceleration g upward (the acceleration due to gravity). The new time of flight is : T T (B*) (C) T (D) 2T 4 2 A stone is projected from horizontal ground. It attains maximum height ‘H’ and strikes a stationary smooth wall and falls on the ground vertically below the maximum height. Assuming the collision to be elastic, the time interval between the stone striking the wall and subsequently striking the ground is

(A)

(A) (C*)

2H g

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14.

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12.

H 2g

(B)

4H g

H

(D) None of these

15.

The slopes of the windscreen of two motor cars are 1 = 30º and 2 = 15º respectively. The cars have velocities v1 and v2 in the horizontal direction. If the hailstones appears to the drivers to be bounced by the windscreen of their v respective cars in the vertical direction then 1 (assuming that hailstones were falling on the cars vertically) is : v2 1 1 (A*) 3 (B) 1 (C) (D) 3 9

16.

A man is sitting inside a moving train and observes the objects outside of the train. Then choose the single correct choice from the following statements : (A) All stationary objects outside the train will move with same angular velocity in opposite direction of the train

PG Brainstormer - 1H with respect to the man. (B*) Stationary objects near the train will move with greater angular velocity & object far from train will move with lesser angular velocity with respect to the man. (C) Large objects like moon or mountains will move with same velocity as that of the train. (D) All of these.

18.

19.

A train travelling at 72 kmh –1 is checked by track repairs. It retards uniformly for 200 m covering next 400 m at constant speed and accelerates to 72 kmh–1 in a further distance of 600 m. If the time at constant lower speed is equal to the sum of the times taken in retarding and accelerating, the total time taken is : (A) 140 s (B) 160 s (C*) 120 s (D) 100 s

 At time t = 0, the velocities of two particles A and B of equal masses and both lying at origin are u A  10 iˆ m/s and  u B  10 3 ˆj m/s respectively. The acceleration of both particles is always constant such that acceleration of A has  magnitude aA = 10 m/s2 and acceleration of B is aB  10 ˆj m/s2. If the centre of mass of system of two particle system moves along a straight line with increasing speed, then the acceleration vector of particle A in m/s2 is : (Assume for a system of two identical particles, their centre of mass lies at the mid point of their line joining) (A*) 5 3 iˆ  5 ˆj (B) 5 iˆ  5 3 ˆj (C) 10 iˆ  5 3 ˆj (D) 5 3 iˆ  10 ˆj Rail is falling vertically with a speed of 20 ms–1. A person is running in the rain with a velocity of 5 ms–1 and a wind is also blowing with a speed of 15 ms–1 (both from the west). The angle with the vertical at which the person should hold his umbrella so that he may not get drenched is :

1 (A*) tan–1  2    20.

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17.

1 (B) tan–1  3   

 4 (C) tan–1  3   

(D) tan–1 (2)

The wind appears to blow from the north to a man moving at speed v in the north-east direction. When he doubles his velocity the wind appears to move from the direction cot–1 (2) east of north. The actual direction of the wind is: 2v towards east

(B)

v towards west 2

(C)

2v towards west

(D*)

v towards east 2

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(A)

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Section - B More than one Choice Correct (Q. No. 21 to 30) The Questions given in this section are MCQs with four answer options (A), (B), (C) and (D) out of which ONE or MORE than ONE answers may be correct. Choose all the correct answer options and fill the answer in the OMR sheet provided at the end. You will get marks in a question only if all the answer options of that question are chosen by you. A cylindrical empty vessel is kept vertical with its open end up, on a horizontal ground. It rains uniformly and vertically. The rate of filling of rain water in the vessel, will : (A) Remain unchanged, if axis of the vessel is made inclined to the vertical (B*) Decreases, if its axis is made inclined with the vertical (C) Decreases, if a slow wind blows (D*) Remains unchanged, if a slow wind blows

22.

A particle of mass m moves on the x-axis as follows : it starts from rest at t = 0 from the point x = 0 and comes to rest at t = 1 at the point x = 1. No other information is available about its motion at intermediate times (0 < t 2 m (C*) y = 3m (D) y = 5 m

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24.

z

5m O

y

x

  River is flowing with a velocity vR = 4 iˆ m/s. A boat is moving with a velocity of vBR = (– 2 iˆ + 4 ˆj ) m/s relative to river. The width of the river is 100 m along y-direction. Choose the correct alternative(s) : (A*) The boatman will cross the river in 25 s (B*) Absolute velocities of boatman is 2 5 m/s (C*) Drift of the boatman along the river current is 50 m (D) The boatman can never cross the river

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26.

2m

Two shells are fired from a cannon with a speed u each, at angles of  and  respectively to the horizontal. The time interval between the shots is T. They collide in mid-air after time t from the first shot. Which of the following conditions must be satisfied ? (A*)  >  (B*) t cos  = (t – T) cos  1 1 (C) (t – T) cos  = t cos  (D*) (u sin ) t – gt2 = (u sin ) (t – T) – g (t – T)2 2 2

28.

A cart moves with a constant speed along a horizontal circular path. From the cart, a particle is thrown up vertically with respect to the cart : (A) The particle will land somewhere on the circular path (B*) The particle will land outside the circular path (C) The particle will follow an elliptical path (D*) The particle will follow a parabolic path

29.

The velocity of a particle moving along a straight line increases according to the linear law v = v0 + kx, where k is a constant. Then : (A*) The acceleration of the particle is k (v0 + kx)

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27.

v  1 loge  1  to attain a velocity v1 k  v0  (C*) Velocity varies linearly with displacement with slope of velocity displacement curve equal to k (D) Data is insufficient to arrive at a conclusion

(B*) The particle takes a time

PG Brainstormer - 1H A man who can swim at a speed v relative to the water wants to cross a river of width d, flowing with a speed u. The point opposite him across the river is P : d (A*) The minimum time in which he can cross the river is v d (B) He can reach the point P in time v d (C*) He can reach the point P in time 2 v  u2 (D*) He cannot reach P if u > v

* *

*

*

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*

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30.

PG Brainstormer - 1H

PG Brain Stormer - 1 H RECTILINEAR MOTION, PROJECTILE MOTION/2D MOTION, RELATIVE MOTION

An Ultimate Tool to understand advanced High School Physics by ASHISH ARORA Sir

Time Allowed Maximum Marks

A B C D 1

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OMR Sheet for the PG Brainstormer - 1H

2

17

3

18

4

19

5

20

6

21

7

22

8

23

9

24

10

25

11

26

12

27

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15

28

CS

13 14

A B C D

16

29 30

90 Min 110

PG Brainstormer - 1H

PG Brain Stormer - 1 H RECTILINEAR MOTION, PROJECTILE MOTION/2D MOTION, RELATIVE MOTION

An Ultimate Tool to understand advanced High School Physics by ASHISH ARORA Sir

Time Allowed

90 Min

Maximum Marks

110

ANSWER KEY Section - A 2. (B) 11. (C) 20. (D)

3. (A) 12. (A)

4. (C) 13. (B)

5. (B) 14. (C)

6. (B) 15. (A)

7. (A) 16. (B)

8. (C) 17. (C)

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1. (D) 10. (B) 19. (A)

9. (B) 18. (A)

Section - B 24. (B) (C) (D)

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21. (B) (D) 22. (A) (C) 23. (A) (B) (C) (D) 28. (B) (D) 29. (A) (B) (C) 30. (A) (C) (D)

25. (A) (C) 26. (A) (B) (C)

27. (A) (B) (D)