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Question Bank No: 2

1. The kinetic energy K of a particle moving in a straight line depends upon the distance s as K= ${as}^{2} .$ The force acting on the particle is

a)		2as
b)		2mas
c)		2a
d)		$\sqrt{{as}^{2}}$

2. A bullet when fired at a target with a velocity of 100m/s penetrates one metre into it. If the bullet is fired at a similar target with a thickness 0.5 metre, then it will emerge from it with a velocity of

a)		50 $\sqrt{2}$ m/s
b)		$\frac{50}{\sqrt{2}}$ m/s
c)		50 m/s
d)		10 m/s

3. If g is acceleration due to gravity on the earth's surface, the gain in potential energy of an object of mass m raised from the surface of the earth to a height equal to radius R of the earth is

a)		mgR
b)		$\frac{1}{2}$ mgR
c)		$\frac{1}{4}$ mgR
d)		2mgR

4. The KE of a body varies directly as the time (t) elapsed. The force acting varies directly as

a)		t
b)		$t^{- 1}$
c)		$t^{1 / 2}$
d)		$t^{- 1 / 2}$

5. The kinetic energy of a body becomes 4 times its initial value. The new linear momentum will be

a)		same as initial value
b)		four times as initial value
c)		twice the initial value
d)		eight times the initial value

6. A ball whose KE is E is projected at an angle of $45^{0}$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

a)		E
b)		E/ $\sqrt{2}$
c)		E/2
d)		zero

7. A stationary particle explodes into two paticles of masses $m_{1}$
and $m_{2,}$ which move in opposite directions, with velocities $v_{1}$ and $v_{2}$ . The ration of their kinetic energies ( $\frac{e_{1}}{e_{2})} is$

a)		$\frac{m_{2}}{m_{1}}$
b)		$\frac{m_{1}}{m_{2}}$
c)		$1$
d)		$\frac{m_{1} v_{2}}{m_{2} v_{1}}$

8. If the momentum of a body increased by 0.01%, then its K.E. will increase by

a)		0.01%
b)		0.02%
c)		0.04%
d)		0.08%

9. When a 1.0 kg mass is attached to a spring of length 50cm, the spring stretches by 2 cm. The mass is pulled down until the length of the spring becomes 60cm. What is the amount of elastic energy stored in the spring in this condition, if g= 10 m/ $s^{2}$

a)		1.5 J
b)		2.0 J
c)		2.5 J
d)		3.0 J

10. Calculate the work done when a force $\vec{F} = 2 \hat{i} + 3 \hat{j} - 5 \hat{k}$
units acts on a body, producing a displacement $\vec{s} + 2 \hat{i} + 4 \hat{j} + 3 \hat{k} units$

a)		30 units
b)		45 units
c)		1 unit
d)		zero unit

11. A uniform chain of length L and mass M is lying on a smooth table and 1/6 of its length is hanging down over the edge of the table. If g is acceleration due to gravity, the work done to pull the hanging part on the table is,

a)		MgL
b)		MgL/6
c)		MgL/18
d)		MgL/72

12. The earth's radius is R and acceleration due to gravity at its surface is g. If a body of mass m falls from a height h= R/ 5 from the earth's surface, its potential energy decreases by

a)		mgh
b)		4/5 mgh
c)		$\frac{5}{6} m g h$
d)		$\frac{6}{7} m g h$

13. A body, constrained to move in y-direction is sujected to a force
$\vec{F} = (- 2 \hat{i} + 15 \hat{j} + 16 \hat{k}) N$
What is the work done by this force in moving the body through a distance of 10 m along the y-axis?

a)		20 J
b)		150 J
c)		160 J
d)		190 J

14. A moving mass of 8 kg collides elastically with a stationary mass of 2kg. If E be the initial kinetic energy of the moving mass, then kinetic energy left with it after the collision will be

a)		0.80 E
b)		0.64 E
c)		0.36 E
d)		0.08 E

15. A 5 kg shell kept at rest suddenly splits into three parts. If two parts of mass 2 kg each are found flying due north and east with a velocity of 5 m/s, what is the velocity of the third part after explosion?

a)		10 m/s due to north east
b)		$\frac{10}{\sqrt{2}}$
c)		10 $\sqrt{2}$ m/s due to south west
d)		10 $\sqrt{2}$ m/s due to south east

16. An engine pumps water continuously through a hole. If the speed with which water passes through the hole nozzle is v and K is the mass per unit length of the water jet as it leaves the nozzle, the rate at which kinetic energy is being imparted to the water is

a)		$\frac{1}{2} K v^{2}$
b)		$\frac{1}{2} K v^{3}$
c)		$\frac{v^{2}}{2 K}$
d)		$\frac{v^{3}}{2 K}$

17. A box of mass 25kg starts from rest and slides down an inclined plane 8 m long and 5 m high. It is found to move at the bottom at 7 m/s. What is the force of attraction?

a)		79.6 N
b)		96.6 N
c)		76.6 N
d)		116.6 N

18. If momentum is increased by 20%, then KE is increased by

a)		44%
b)		55%
c)		66%
d)		77%

19. A bullet when fired at a target with a speed of 100 m/s penetrates one metre into it, If the bullet is fired at a similar target with a thickness of 25 cm, then it will emerge with a speed of

a)		$\frac{100}{\sqrt{2}} m / s$
b)		100 $\times$ $\frac{2}{\sqrt{3}} m / s$
c)		100 $\times \frac{\sqrt{3}}{2} m / s$
d)		100 $\times \frac{2}{\sqrt{5}} m / s$

20. A body is dropped from a height h. If it acquires a momentum p, then the mass of body is

a)		$\frac{P}{\sqrt{2 gh}}$
b)		$\frac{P^{2}}{2 gh}$
c)		$\frac{2 gh}{p}$
d)		$\sqrt{\frac{2 gh}{p}}$

21. The potential energy of a certain spring when stretched through a distance s is 10 joule. The amount of work in joule that must be done on this spring to stretch it through additional distance s will be

a)		30
b)		40
c)		10
d)		20

22. The kinetic energy acquired by a mass m in travelling a certain distance d, starting from rest under the action of a constant force, is directly proportional to

a)		$\sqrt{m}$
b)		independent of m
c)		$\frac{1}{\sqrt{m}}$
d)		m

23. A bus can be stopped by applying a retarding force F when it is moving with a speed v on a level road. The distance covered by it before coming to rest is s. If the load of the bus increases by 50% because of passengers for the same speed and same retarding force, the distance covered by the bus to come to rest shall be

a)		1.5 s
b)		2 s
c)		1 s
d)		2.5 s

24. A bullet when fired at a target with a velocity decreased to 50% after penetrating 30cm into it. Then the additional thickness it will penetrate in cm before coming to rest is

a)		10 cm
b)		30 cm
c)		40 cm
d)		60 cm

25. Two bodies with mass $M_{1}$ and $M_{2}$ have equal momenta then the kinetic energies of first and second bodies are in the ratio.

a)		$M_{1}$ : $M_{2}$
b)		$M_{2}$ : $M_{1}$
c)		$M_{1}^{2}$ : $M_{2}^{2}$
d)		$\sqrt{M_{2}}$ : $\sqrt{M_{2}}$

26. Two bodies of different masses $M_{1}$ and $M_{2}$ have equal kinetic energies. Their respective momenta $P_{1}$ and $P_{2}$ are in the ratio

a)		$M_{1} : M_{2}$
b)		$\sqrt{M_{1}} : \sqrt{M_{2}}$
c)		$M_{2} : M_{1}$
d)		$\sqrt{M_{2}} : \sqrt{M_{1}}$

27. The power developed by a student of mass 50 kg climbing up a vertical path at the rate 2 ${ms}^{- 1}$ is

a)		98 watts
b)		980 joules
c)		9.8 watts
d)		980 watts

28. The kinetic energy of a body of mass m is related to its linear momentum (P) by the relation

a)		KE = 2 $p^{2} / m$
b)		KE = $P^{2} / m$
c)		KE = $P^{2} / 2 m$
d)		KE = 2 $m / P^{2}$

29. A force of 40N acting continuously increases the KE of an object from 200J to 600J. The distance moved by the object is

a)		400 m
b)		60 m
c)		200 m
d)		10 m

30. An electric motor while lifting a given load produces a tension of 4,500 N in the cable attached to the load. If the motor winds the cable at the rate of 2 ${ms}^{- 1}$ , then the power must be

a)		9kW
b)		225W
c)		15kW
d)		9kW

31. A thief stole a box full of valuable articles of weight W and while carrying it on his head jumped down from a wall of height h from the ground. Before he reached the ground he experienced a load of

a)		2W
b)		zero
c)		W
d)		W/h

32. A body of mass 1 kg and momentum 2N s has kinetic energy

a)		2J
b)		1J
c)		5J
d)		8J

33. A train to move on horizontal surface with constant velocity of 60 ${ms}^{- 1}$ , requires an engine of 7500 W power. The force offered by the engine is

a)		1,500 N
b)		125 N
c)		1, 200 N
d)		750 N

34. The PE of a spring when stretched through a distance is 10 joules. The amount of work done to stretch it through twice the distance will be

a)		40 J
b)		30 J
c)		10 J
d)		20 J

35. A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

a)		$t^{1 / 2}$
b)		$t^{3 / 4}$
c)		$t^{3 / 2}$
d)		$t^{2}$

36. A chain of length L and mass M is lying on a smooth table and one- third of the length is hanging vertically down over the edge of the table. If g is the acceleration due to gravity, the work required to pull the hanging part on to the table is

a)		MgL
b)		MgL/18
c)		MgL/9
d)		MgL/3

37. A long spring is stretched by 0.02 m, the PE = U. If the spring is stretched by 0.1 m, the PE stored is

a)		U/25
b)		U/5
c)		5U
d)		25 U

38. A body falls freely under gravity. If its speed is $v$ when it has lost an amount U of gravitational potential energy, then its mass is

a)		$U^{2} g / v^{2}$
b)		$U^{2} / g$
c)		$U / v^{2}$
d)		$2 U / v^{2}$

39. A motor car needs an engine 7.5 kW to keep it moving with constant speed of 20 ${ms}^{- 1}$ on a horizontal road. The force of friction between the tyre and the ground is

a)		$1.5 \times 10^{2} N$
b)		375 N
c)		$1.5$ $\times$ $10^{5} N$
d)		3.75 N

40. The kinetic energy of a body is increased by 300%. Then the momentum of the body will increase by

a)		300 %
b)		150 %
c)		100 %
d)		50 %

41. Two masses 1kg and 4kg are moving with equal KE. The ratio of the magnitudes of their momenta is

a)		4 : 1
b)		$\sqrt{2 : 1}$
c)		2 : 4
d)		1 : 2

42. A uniform rod of length 4m and mass 10 kg lies on ground horizontally. The work done in joules to make it stand vertical on the ground is

a)		96 J
b)		20 J
c)		98 J
d)		196 J

43. A 10 kg stone is suspended with a rope of breaking tension 30 kg wt. The minimum time in which it can be raised through a height of 10 m starting from rest is (g = ${10 ms}^{- 2}$ )

a)		0.5 s
b)		1.0 s
c)		$\sqrt{2 / 3}$ s
d)		2 s

44. A cricket ball is hit from the ground level at an angle of $45^{\circ}$ with the horizontal and has kinetic energy E. The kinetic energy at the highest point of its path is

a)		zero
b)		E/ $\sqrt{2}$
c)		$\sqrt{2 / 3}$
d)		E/2

45. The magnitude of the momentum of a particle is increased by 100%. Increase in kinetic energy is

a)		100%
b)		200%
c)		300%
d)		400%

46. A body is released from a great height and falls freely towards the earth. Another body is released from same height exactly one second later. Then the separation between the two bodies, two seconds after the release of the second body is

a)		4.9 m
b)		9.8 m
c)		19.6 m
d)		24.5 m

47. A boat crosses the river in shortest possible time. The speed of the boat in still water is 13 m/s. The average speed of the boat while crossing the river comes out to be 12 m/s. What is the velocity of the flow of river?

a)		2 m/s
b)		5 m/s
c)		6 m/s
d)		none of the above

48. A uniform chain of length L and mass M is lying on a smooth table such that one third of its length is hanging vertically down over the edge of the table. If g is the acceleration due to gravity, then the work required to pull the hanging part is on to the table is

a)		$MgL$
b)		$\frac{MgL}{3}$
c)		$\frac{MgL}{9}$
d)		$\frac{MgL}{18}$

49. Two masses of 1g and 4g are moving with equal kinetic energies. The ratio of their linear momenta is

a)		4:1
b)		$\sqrt{2} : 1$
c)		1:2
d)		1:16

50. A ball is thrown vertically upwards upwards from the top of tower at 4.9 m/s. It strikes the point near the base on the lower after 3 seconds. The height of the tower is

a)		73.5 m
b)		44.1 m
c)		29.4 m
d)		4.9 m