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Page 1 of 2 CONSERVATION OF MOMENTUM 1. A sphere of mass ‘m’ moving with velocity ‘u’ makes a direct collision with another sphere of mass ‘2m’ at rest. If the collision is perfectly elastic, find (a) the velocity of the first sphere (b) the impulse on the first sphere 2. Two bodies of mass 6 kg and 4 kg move in opposite directions with velocities of 9 m/s and 7 m/s, respectively. Compute the resultant velocity on collision if they stick together. 3. Two balls ‘A’ and ‘B’ weighing 6 N and 4 N each approach each other with speeds of 2 m/s and 3.5 m/s, respectively. On the assumption of perfect collision, what will be their velocities after collision? 4. A 100 g ball makes an elastic head-on collision with a ball of unknown mass that is initially at rest. If the 100 g ball rebounds at one-third its original speed, what is the unknown mass? 5. A body of mass 4 kg moves with a velocity of 2 m/s and collides head-on with another body of mass 3 kg moving in the opposite direction with a velocity of 5 m/s. After the collision both the bodies move off together with velocity ‘v’. Calculate (a) the total momentum before collision (b) the velocity ‘v’. 6. A 2 kg mass ‘A’, travelling in a straight line with velocity 4 m/s collides with a stationary 1 kg mass ‘B’. The two masses stick together and move in the same straight line after collision. (a) What is the velocity of the composite mass after impact? (b) What is the loss of kinetic energy in the collision? What happens to the lost energy? (c) If the impact lasted 0.1 s, what is the average force experienced by ‘B’ during collision? 7. A machine gun fires 90 bullets per minute with a velocity of 800 m/s. If each bullet has a mass of 0.075 kg, what average force would be required to hold the gun? 8. Radium atoms are radioactive. A stationary radium atom (mass = 226 amu) shoots out an alpha particle (mass = 4 amu) with a speed of 1.5 10 7 m/s. Find the speed of the residual atom. 9. A shell moving at 75 m/s bursts into two parts. The smaller part is 1/25th of the whole and the bigger part is stopped dead. Find the velocity of the remainder. 10. Two skaters whose masses are 40 kg and 80 kg are at rest at the centre of a large skating rink. They push away from each other and the skater with the 40 kg mass moves off at 1.2 m/s. What is the speed of the other? 11. A 20 g bullet is fired from a 5 kg rifle with a muzzle velocity of 800 m/s. What is the recoil velocity of the rifle? Compare the kinetic energies of the rifle and the bullet. 12. A ballistics pendulum is a block of mass 3 kg suspended by a string 2.5 m long. A bullet of mass 9 g strikes the block and gets embedded in it. As a result the block rises such that the string now makes an angle of 18˚ with the vertical. Find the speed of the bullet. 13. A 10 g bullet fired from a rifle travels horizontally, strikes a 5 kg block of wood, and gets embedded in it. The impact causes the block to swing to a height of 5 cm above its initial level. Calculate the speed of the bullet. 14. A wooden block of mass 10 g is dropped form the top of a cliff 100 m high. At the same time a bullet of mass 10 g is fired from the foot of the cliff vertically upwards with a velocity of 100 m/s. (Take g = 10 m/s2) (a) Where and when will they meet? (b) If the bullet, after striking the block, gets embedded in it, how high will rise above the cliff before it starts falling? Assume that the block does not rise appreciably during impact. 15. A small ball ‘A’ slides down the quadrant of a circle as shown in the figure below and hits the ball ‘B’ of equal mass, which is initially at rest. Find the velocities of both balls after collision. Neglect the effect of friction and assume the collision to be elastic. Page 2 of 2 16. (Calculus based) A rocket having initial mass ‘mo’ starts from rest. Fuel of mass ‘m’ has been ejected when the rocket attains a velocity ‘v’. If the exhaust velocity is always ‘ve’ relative to the mo rocket, show that v v e ln mo m 17. A shell explodes into three fragments of equal masses. If two fragments travel at right angles to one another with equal speeds, what is the direction and speed of the third fragment? 18. Sand particles drop at the rate of 1000 kg per minute from the bottom of a hopper onto a conveyor belt moving horizontally at a constant speed of 3.6 m/s. Find the force required to drive the conveyor belt. Neglect friction. 19. A 6.0 kg sledge is travelling across ice at a constant speed of 9 m/s. A 1.2 kg package is dropped into it vertically. Describe the subsequent motion. 20. A motor pumps water at such a rate that a jet of water strikes a wall normally with a speed of 12 m/s. If after striking the wall the water spreads parallel to the wall, calculate the pressure on the p mv Avt F v v 2 wall. H int : P A At t At 21. A bullet of mass 2 g travelling horizontally with a speed of 500 m/s strikes a block of mass 1 kg initially at rest on a rough horizontal surface. The bullet passes through the block and emerges out with a velocity of 100 m/s and the block slides a distance of 20 cm. Find: (a) The coefficient of friction between the block and the surface (b) The decrease in the kinetic energy of the bullet (c) Kinetic energy of the block at the instant after the bullet passes through it. Answers 1 4 (1) u, mu 3 3 (2) 2.6 m/s (3) – 2.4 m/s, 3.1 m/s (4) 200 g (5) – 7kg.m/s, - 1 m/s (6) 2.67 m/s, 5.33 J, 26.7 N (7) 90 N (8) 2.7 10 5 m/s (15) 0, 1.4 m/s (9) 1875 m/s (16) (10) 0.6 m/s (17) (11) 3.2 m/s (18) 60 N (12) 520 m/s (19) 7.5 m/s (13) 501 m/s (20) 1.44 10 5 N/m2 (14) 1 s, 95 m, 75 m (21) 0.16, 240 J, 0.32 J 2v , 135˚ or 225˚