LEVEL – I

Q:1. If the KE of a body becomes four times of its initial value, then the new momentum will be more than its initial momentum by;

(A) 50%

(B) 100%

(C) 125%

(D) 150%

Q:2. A bullet in motion hits and gets embedded in a solid block resting on a frictionless table. What is conserved?

(A) Momentum and KE

(B) Kinetic energy alone

(C) Neither KE nor momentum

(D) Momentum alone

Q:3. The centre of mass of a body:

(A) Lies always at the geometrical center

(B) Lies always inside the body

(C) Lies always outside the body

(D) Lies within or outside the body

Q:4. The spacecraft of mass M moves with velocity V in free space at first, then it explodes breaking into two pieces. If after explosion a piece of mass m comes to rest, the other piece of space craft will have a velocity:

(A) MV/(M – m)

(B) MV/(M + m)

(C) mV/(M – m)

(D) mV/(M + m)

Q:5. A bomb travelling in a parabolic path under the effect of gravity, explodes in mid air. The centre of mass of fragments will:

(A) Move vertically upwards and then downwards

(B) Move vertically downwards

(C) Move in irregular path

(D) Move in the parabolic path the unexploded bomb would have traveled

Q:6. If a ball is thrown upwards from the surface of earth:

(A) The earth remains stationary while the ball moves upwards

(B) The ball remains stationary while the earth moves downwards

(C) The ball and earth both moves towards each other

(D) The ball and earth both move away from each other

Q:7. Fast neutrons can easily be slow down by

(A) The use of lead shield.

(B) Passing them through heavy water.

(C) Elastic collision with heavy nucleus

(D) Applying a strong electric field.

Q:8. A body is hanging from a rigid support by an inextensible string of length ‘l’ . It is struck inelastically by an identical body of mass m with horizontal velocity

v = √(2gL) , the tension in the string increases just after the striking by (A) mg

(B) 3 mg

(C) 2 mg

(D) None of these

Q:9. A bullet weighing 10 gm and moving at 300 m/s strikes a 5 kg ice and drops dead. The ice block is sitting on a frictionless level surface. The speed of the block after the collision, is

(A) 6 cm/sec

(B) 6 m/sec

(C) 60 mc/sec

(D) 60 m/sec.

Q:10. A massive ball moving with speed v collides with a tiny ball having a mass very much smaller than the mass of the first ball. If the collision is elastic, then immediately after the impact, the second ball will move with a speed approximately equal to:

(A) v

(B) 2v

(C) v/2

(D) ∞

__ANSWER:__

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

LEVEL – I

Q:11. A bag of mass M hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined system (bag + bullet):

(A) Momentum is mMv/(M + m)

(B) KE is (1/2) Mv^{2}

(C) Momentum is mv

(D) KE is m^{2}v^{2}/2(M + m)

Q:12. A surface is hit elastically and normally by n balls per unit time, all the balls having the same mass m and moving with the same velocity u. The force on the surface is:

(A) mnu^{2}

(B) 2mnu

(C) (1/2)mnu^{2}

(D) 2mnu^{2}

Q:13. A bullet of mass m hits a target of mass M hanging by a string and gets embedded in it. If the block rises to a height h as a result of this collision, the velocity of the bullet before collision is:

(A) $ \displaystyle v = \sqrt{2 g h} $

(B) $ \displaystyle v = \sqrt{2 g h} (1 + m/M) $

(C) $ \displaystyle v = \sqrt{2 g h} (1 + M/m) $

(D) $ \displaystyle v = \sqrt{2 g h} (1 – m/M) $

Q:14. Two particles of mass M and 2 M are at a distance D apart. Under their mutual force they start moving towards each other. The acceleration of their centre of mass when they are D/2 apart is:

(A) 2 GM/D^{2}

(B) 4 GM/D^{2}

(C) 8 GM/D^{2}

(D) Zero

Q:15. A body of mass 1 kg initially at rest, explodes and breaks into three fragments of mass in the ratio 1 : 1 :3. The two pieces of equal mass fly off perpendicular to each other with speed of 15 m/sec. each. The speed of havier fragment is:

(A) 5√2 m/s

(B) 45 m/se

(C) 5 m/s

(D) 156 m/s

Q:16. A sphere of mass m1 = 2kg collides with a sphere of mass m2 = 3kg which is at rest. Mass m1 will move at right angle to the line, joining centres at the time of collision, if the coefficient of restitution is

(A) 4/9

(B) 1/2

(C) 2/3

(D) √(2/3)

Q:17. In a free space, a rifle of mass M shoot a bullet of mass m at a stationary block of mass M distance D away from it. When the bullet has moved through a distance d towards the block, the centre of mass of the bullet-block system is at a distance from rifle of

(A) m(D-d)/(M+m)

(B) d(M+m)/M from a rifle

(C) (md+MD)/(M+m)

(D) None of these.

Q:18. Two identical billiard balls are in contact on a table. A third identical ball strikes them symmetrically and come to rest after impact. The restitution is

(A) 2/3

(B) 1/3

(C) 1/6

(D) √3/2

Q:19. A sphere of mass m moving with a constant velocity hits another stationary sphere of the same mass. If e is the coefficient of restitution, then ratio of velocities of the two spheres after collision will be:

(A) (1-e)/(1+e)

(B) (1+e)/(1-e)

(C) (e+1)/(1+e)

(D) (e-1)/(e+1)

Q: 20. A neutron travelling with a velocity v and kinetic energy E collides elastically head on with the nucleus of an atom of mass number A at rest. The fraction of total energy retained by the neutron is:

(A) $ \displaystyle (\frac{A-1}{A+1})^2 $

(B) $ \displaystyle (\frac{A+1}{A-1})^2 $

(C) $ \displaystyle (\frac{A-1}{A})^2 $

(D) $ \displaystyle (\frac{A+1}{A})^2 $

__ANSWER:__

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