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Question Bank No: 4

1. If the horizontal range of a particle is four times its maximum height, the angle of projection is

a)		$30^{0}$
b)		$45^{0}$
c)		$60^{0}$
d)		$\sin - 1 \frac{1}{4}$

2. The range of a projectile, thrown with an initial speed u at an angle of projection $15^{0}$ is R. What will be the ratio of their initial speed 2u at an angle $30^{0}$

a)		2R
b)		$2 \sqrt{3} R$
c)		4R
d)		$4 \sqrt{3} R$

3. Two balls are projected in direction at $30^{0}$ and $60^{0}$ with the horizontal. If both attain the same height and ratio of their initial speed is

a)		$\sqrt{3 : 1}$
b)		$1 : \sqrt{3}$
c)		$\sqrt{3 : 2}$
d)		$2 : \sqrt{3}$

4. The angle of projection of a projectile is $30^{0} .$ The ratio of the horizontal range and the maximum height is

a)		$4 \sqrt{3}$
b)		$3 \sqrt{3}$
c)		$2 \sqrt{3}$
d)		$3 \sqrt{3}$

5. It is possible to project a particle with a given speed in two possible ways so that it has the same horizontal range R. The product of the times taken by it in the two possible way is

a)		$\frac{R}{g}$
b)		$\frac{2 R}{g}$
c)		$\frac{3 R}{g}$
d)		$\frac{4 R}{g}$

6. A ship of mass $3 \times 10^{7}$ kg initially at rest is pulled by a force of $5 \times 10^{4} N$ through a distance of 3m. Assuming that the resistance due to water is negligible the speed of the ship is

a)		1.5m/s
b)		5 m/s
c)		0.1 m/s
d)		6 m/s

7. When a force of IN acts on a 1 kg body that is able to move freely, the body receives

a)		a speed of 1 m/s
b)		an acceleration of 1 $m / s^{2}$
c)		an acceleration of 9.8 $m / s^{2}$
d)		a momentum of 9.8NS

8. A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m by applying a force p at one end of the rope. The force which the rope exerts on the block is

a)		$\frac{P}{M - m}$
b)		$\frac{PM}{M + m}$
c)		$\frac{Pm}{M + m}$
d)		Pm(M+m)

9. An elevator is moving vertically up with an acceleration 'a'. The force exerted on the floor by a passenger of mass m is

a)		mg
b)		ma
c)		mg-ma
d)		mg+ma

10. The minimum acceleration with which a fireman can slide down a rope of breaking strength two-third of his weight is

a)		zero
b)		$g / 3$
c)		3g
d)		g

11. A body kept on a smooth inclined plane having inclination 1 in x will remain stationary relative to the inclined plane if the plane is given a horizontal acceleration equal to

a)		$g / \sqrt{x^{2} - 1}$
b)		$gx \sqrt{x^{2} - 1}$
c)		$\sqrt{x^{2} - 1 / gx}$
d)		$\sqrt{x^{3} - 1 / gx}$

12. A ball of mass 0.1kg strikes a wall normally with a speed of 30 m/s and rebounds with a speed of 20m/s. The impulse of the force exerted by the wall on the ball is

a)		1N-S
b)		5N-S
c)		2N-S
d)		3N-S

13. A ball of mass m is thrown upward with a velocity $v .$ If air exerts an average resisting force F, the velocity with which the ball returns back to the thrower is

a)		$v \sqrt{\frac{mg}{mg + F}}$
b)		$v \sqrt{\frac{F}{mg + F}}$
c)		$v \sqrt{\frac{mg - F}{mg + F}}$
d)		$v \sqrt{\frac{mg + F}{mg - F}}$

14. A body takes n times as much time to slide down as $45^{0}$ rough incline as it takes to slide down a smooth $45^{0}$ incline. The coefficient of friction is

a)		$1^{- 1} / n 2$
b)		$1 / 1 - n 2$
c)		$\sqrt{1 - 1 / n 2}$
d)		$1 / \sqrt{1 - n^{2}}$

15. A bullet of mass a and velocity b is fired into a large block of mass c. The final velocity of the system is

a)		$\frac{cb}{a + b}$
b)		$\frac{ab}{a + c}$
c)		$\frac{(a + b) a}{c}$
d)		$\frac{(a + c) b}{a}$

16. If a force $\vec{F}$ applied on a body moves it with a velocity $\vec{v},$ then the power will be

a)		$\vec{F} / \vec{v}$
b)		$F / \vec{v}$
c)		$F \vec{v}$
d)		$\vec{F} . \vec{v}$

17. A 120 g mass has a velocity $\vec{v} = (2 î + 5 ĵ) m / s$ at a certain instant. Its kinetic energy is

a)		3J
b)		4J
c)		5J
d)		1.74J

18. 2 equal masses $m_{1} and m_{2}$ moving along same straight line with velocities $+ 3 m / s and - 5 m / s$ respectively collide elastically. Their velocities after collision will be respectively

a)		+4 m/s for both
b)		-3m/s and +5m/s
c)		-4m/s and +4m/s
d)		5m/s and +3m/s

19. Which of the following is not conserved in inelastic collision

a)		momentum
b)		kinetic energy
c)		both momentum and kinetic energy
d)		neither kinetic energy nor momentum

20. A car moving with a speed of 40km/h can be stopped by applying brakes after atleast 2m. If the same car is moving with a speed of 80km/h, what is the minimum stopping distance?

a)		8m
b)		6m
c)		4m
d)		7m

21. A 4 kg mass and 1kg mass are moving with equal kinetic energies. The ratio of their momenta is

a)		1:2
b)		1:1
c)		2:1
d)		4:1

22. An object of mass 40kg and having velocity 4m/s collides with another object of mass 60kg, having velocity 2m/s. The loss of energy when the collision is perfectly inelastic is

a)		392J
b)		440J
c)		48J
d)		110J

23. A force $({mv}^{2} / r)$ is acting on a body of mass m moving with velocity v in a circle of radius r. What is the work done by the force in moving the body over half the circumference of the circle.

a)		$\frac{{mv}^{2}}{r} \times π r$
b)		0
c)		$\frac{{mv}^{2}}{r^{2}}$
d)		$\frac{π r^{2}}{{mv}^{2}}$

24. A car of mass m is driven with acceleration 'a' along a straight level road against a constant external resistive force R. When velocity of the car is v, the rate at which engine of car is doing work will be

a)		Rv
b)		mav
c)		$(R + ma) v$
d)		(ma-R)v

25. The bob A of simple pendulum is released when the string makes an angle of $45^{0}$ with the vertical. It hits another bob B of the same material and mass kept at rest on the table. If the collision is elastic

a)		both A and B raise to the same height
b)		both A and B come to rest at B
c)		both A and B move with the velocity of A
d)		A comes to rest and B moves with the velocity of A

26. A body of weight mg is hanging on a string, which extends its length by l. The work done in extending the string is

a)		1/2 mgl
b)		mg/2
c)		2mgl
d)		none of these

27. If water falls from a dam into a turbine wheel 19.6m below, the velocity of water at turbine is $(take g = 9.8 m / s^{2})$

a)		9.8 m/s
b)		19.6 m/s
c)		39.2 m/s
d)		98 m/s

28. A body of mass 100g is rotating in a circular path of radius r with constant speed. The work done in one complete revolution is

a)		100r J
b)		r/100 J
c)		100/r J
d)		0

29. A 600 kg rocket is set for a vertical firing. If the exhaust speed is 1000 m/s, the mass of the gas ejected per second to supply the thrust needed to overcome the weight of rocket is

a)		117.6 kg/s
b)		58.6 kg/s
c)		6kg/s
d)		76.4 kg/s

30. An impulse is supplied to a moving object with the force at an angle of $20^{0}$ with respect to velocity vector. The angle between the impulse vector and the change in momentum vector is

a)		$0^{0}$
b)		$60^{0}$
c)		$70^{0}$
d)		$240^{0}$

31. A man of mass 90kg is standing in an elevator whose cable broke suddenly, if the elevator falls, apparent weight of the man is

a)		90N
b)		90gN
c)		0N
d)		any negative value

32. The average force necessary to stop a hammer with 25Ns momentum is 0.05s expressed in n is

a)		500
b)		125
c)		50
d)		25

33. Physical independence of a force is a consequence of

a)		Third Law of Motion
b)		Second Law of Motion
c)		First Law of Motion
d)		All of these Laws

34. A stretching force of 10N is applied at one end of a spring balance and an equal stretching force is applied at the other end at the same time, what will be the reading of the balance?

a)		5N
b)		10N
c)		20N
d)		0

35. The coefficient of static friction between two surfaces depends upon

a)		the normal reaction
b)		the shape of the surfaces in contact
c)		the area of contact
d)		none of the above

36. A scooter of mass 120 kg is moving with a uniform velocity of 108 km/h. The force required to stop the vehicle in 10s is

a)		360N
b)		720N
c)		180N
d)		20X10.8N

37. A shell is fired from a canoon, it explodes in mid air, its total

a)		momentum increases
b)		momentum decreases
c)		kinetic energy increases
d)		kinetic energy decrease

38. A block at rest explodes into three parts of the same mass, the momentum of the two parts are 2p $î$ and p $ĵ .$ The momentum of the third part will have a magnitude

a)		p
b)		$p \sqrt{3}$
c)		$p \sqrt{5}$
d)		0

39. M be the mass of a body at the surface of earth. What is the weight of the object at the centre of the earth?

a)		0
b)		3.9N
c)		5N
d)		4.9N

40. A monkey is descending from the branch of tree with constant acceleration if the braking strength is 75% of the weight of the monkey, the minimum acceleration with which the monkey can slide down without breaking the branch is

a)		g
b)		3g/4
c)		g/4
d)		g/2

41. A ball weighing 10g hits a hard surface vertically with a speed of 5m/s and rebounds with the same speed the ball remains in contact with the surface for 0.01s. The average force exerted by the surface on the ball is

a)		100N
b)		10N
c)		1N
d)		0.1N

42. A block has been placed on a inclined plane with the slope angle Q, block slides down the plane at constant speed. The coefficient of kinetic friction is

a)		sin Q
b)		cos Q
c)		g
d)		tan Q

43. A block of mass 2kg is placed on the floor, the coefficient of static friction is 0.4 . If a force of 2.8N is applied on the block parallel to floor, the force friction between the block and floor (taking g =10 $m / s^{2}$ ) is

a)		2.8N
b)		8N
c)		2N
d)		0

44. A bullet of mass m and velocity $a$ is fired into a large block of wood of mass M. The final velocity of system is

a)		$\frac{a}{m + a} a$
b)		$\frac{m + M}{m} a$
c)		$\frac{m + a}{M}$
d)		$\frac{m}{m + M} a$

45. A body of mass 2kg collides with a wall with speed 100m/s and rebounds with same speed. If time of contact was 1/50s, the force exerted on wall is

a)		8N
b)		$2 \times 10^{4} N$
c)		4N
d)		$10^{4} N$

46. A Wagon weighing 1000kg is moving with velocity of 50km/h on smooth horizontal rails. A mass of 250 kg is dropped into it, the velocity with which it moves now is

a)		12.5km/h
b)		20km/h
c)		40km/h
d)		50km/h

47. In a rocket of mass 1000kg, fuel is consumed at a rate of 40kg/s. The velocity of gas ejected from rocket is $5 \times 10^{4} m / s$ . The thrust on rocket is

a)		$2 \times 10^{3} N$
b)		$5 \times 10^{4} N$
c)		$2 \times 10^{6} N$
d)		$2 \times 10^{8} N$

48. A person is sitting in a traveling train and facing engine. He tosses up a coin and coin falls behind him. It can be concluded that train is

a)		moving forward and gaining speed
b)		moving forward and losing speed
c)		moving forward with uniform speed
d)		moving backward with uniform speed

49. If a force of 250N act on body, the momentum acquired is 125kg m/s. what is the period for which force act on the body

a)		0.5s
b)		0.2s
c)		0.4s
d)		0.25s

50. A bullet of mass 0.1kg is fired with a speed of 100m/s, the mass of gun is 50kg. The velocity of recoil is

a)		0.2m/s
b)		0.1 m/s
c)		0.5 m/s
d)		0.05m/s