LEVEL – I

Q:1. Two bodies of masses m1 and m2 have equal momenta. Their kinetic energies E1 and E2 are in the ratio:

(A) √m_{1} : √m_{2}

(B) m_{1} : m_{2}

(C) m_{2} : m_{1}

(D) m_{1}^{2} : m_{2}^{2}

Q:2. A chain of mass M, length l hangs from a pulley. If it is wound such that half of the chain remains overhung, the work done by the external agent is equal to

(A) Mgl/2

(B) (3/4)Mgl

(C ) (3/8)Mgl

(D) None of these

Q:3. A block of mass m is suspended by a light thread from an elevator. The elevator is accelerating upward with uniform acceleration a. The work done during t secs by the tension in the thread is:

(A)$ \displaystyle \frac{m}{2}(g+a)a t^2$

(B) $ \displaystyle \frac{m}{2}(g-a)a t^2$

(C) $ \displaystyle \frac{m}{2}g a t^2$

(D) 0

Q:4. It is easier to draw up a wooden block along an inclined plane than to haul it vertically, principally because:

(A) the friction is reduced

(B) the mass becomes smaller

(C) only a part of the weight has to be overcome

(D) ‘g’ becomes smaller

Q:5. A motor boat is travelling with a speed of 3.0 m/sec. If the force on it due to water flow is 500 N, the power of the boat is:

(A) 150 KW

(B) 15 KW

(C) 1.5 KW

(D) 150 W

Q:6. Two masses of 1 gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is:

(A) 4 : 1

(B) √2 : 1

(C) 1 : 2

(D) 1 : 16

Q:7. A system of two bodies of masses m and M being interconnected by a spring of stiffness k moves towards a rigid wall with a K.E. E . If the body M sticks to the wall after the collision, the maximum compression of the spring will be

(A) $ \displaystyle \sqrt{\frac{m E}{k}}$

(B) $ \displaystyle \sqrt{\frac{2 m E}{(M+m)k}}$

(C) $ \displaystyle \sqrt{\frac{2 m E}{M k}}$

(D)$ \displaystyle \sqrt{\frac{2 M E}{(M+m)k}}$

Q:8. Two identical blocks each of mass m being interconnected by a light spring of stiffness k is pushed by a force F as shown in the figure. The maximum potential energy stored in the spring is equal to:

(A) F^{2}/2K

(B) F^{2}/4K

(C) F^{2}/8K

(D) None of these

Q:9. A stone tied to a string of length l is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude in its velocity as it reaches a position, where the string is horizontal, is

(A) $ \displaystyle \sqrt{u^2 – 2g l }$

(B) $ \displaystyle \sqrt{ 2g l }$

(C) $ \displaystyle \sqrt{u^2 – g l }$

(D)$ \displaystyle \sqrt{2 (u^2 – g l) }$

Q:10. A cord is used to raise a block of mass m vertically through a distance d at a constant downward acceleration g/4. The work done by the chord is

(A) mgd/4

(B) 3Mgd/4

(C) -3Mgd/4

(D) Mgd

__ANSWER:__

1. (C) 2. (C) 3. (A) 4. (C) 5. (C) 6. (C) 7. (B) 8. (A) 9. (D) 10. (B)

LEVEL – I

Q:11. A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part onto the table is:

(A) MgL

(B) MgL/3

(C) MgL/9

(D) MgL/18

Q:12. An engine pumps a liquid of density ‘d’ continuously through a pipe of area of cross-section A. If the speed with which the liquid passes through a pipe is v, then the rate of liquid flow is

(A) Adv^{3}/2

(B) (1/2) adv

(C) Adv^{2}/2

(D) Adv^{2}

Q:13. A body of mass m accelerates uniformly from rest to v1 in time t1. As a function of t, the instantaneous power delivered to the body is:

(A) mv_{1}/t_{1}

(B) mv_{1}^{2}/t_{1}

(C) mv_{1}t^{2}/ t_{1}

(D) mv_{1}^{2}t/t_{1}^{2}

Q:14. A man M1 of mass 80 Kg runs up a staircase in 15 s. Another man M2 also of mass 80 Kg runs up the stair case in 20 s. The ratio of the power developed by them will be:

(A) 1

(B) 4/3

(C) 16/9

(D) None of the above

Q:15. How much work is done in raising a stone of mass 5 Kg and relative density 3 lying at the bed of a lake through height of 3 meter? (Take g = 10 ms-2):

(A) 25 J

(B) 100 J

(C) 75 J

(D) None of the above

Q:16. A person is pulling a mass m from ground on a rough hemispherical surface upto the top of the hemisphere with the help of a light inextensible string as shown in the figure. The radius of the hemisphere is R. The work done by the tension in the string is:

(A) mgR(1 + μ)

(B) μmgR

(C) mgR(1-μ)

(D) μmg(R/2).

Q:17. A small mass m is sliding down on a smooth curved incline from a height h and finally moves through a horizontal smooth surface. A light spring of force constant k is fixed with a vertical rigid stand on the horizontal surface, as shown in the figure. The maximum compression in the spring if the mass m released from rest from the height h and hits the spring on the horizontal surface is:

(A) $ \displaystyle \sqrt{\frac{2 m g h}{k} }$

(B) $ \displaystyle \sqrt{\frac{ m g h}{k} }$

(C) $ \displaystyle \sqrt{\frac{ m g h}{2 k} }$

(D) None of these.

Q:18. A block of mass m moves towards a light spring of stiffness k on a smooth horizontal plane. If it compresses the spring through a distance x0, the magnitude of total change in momentum of the block is:

(A) $ \displaystyle 2 \sqrt{k m } x_0 $

(B) 0

(C) $ \displaystyle \sqrt{k m } x_0 $

(D) $ \displaystyle -2 \sqrt{k m } x_0 $

Q:19. If v, P and E denote the velocity, momentum and kinetic energy of the particle, then:

(A) P = dE/dv

(B) P = dE/dt

(C) P = dv/dt

(D) none of these

Q:20. Energy required to accelerate a car from 10 to 20 m/s compared with that required to accelerate from 0 to 10 m/s is

(A) twice

(B) four times

(C) three times

(D) same

__ANSWER:__

11. (D) 12. (D) 13. (D) 14. (B) 15. (B) 16. (A) 17. (A) 18. (C) 19. (A) 20. (C)