Title CENTRE OF MASS & COLLISIONS.pdf ✅

Centre of Mass & Collisions  Digital www.allendigital.in [ 79 ] MOTION OF CENTRE OF MASS 10. The law of conservation of momentum for a system is based on Newton’s :– (1) First law of motion (2) Second law of motion (3) Third law of motion (4) Law of gravitation 11. A person of mass m is standing on one end of a plank of mass M and length L and floating in water. The person moves from one end to another and stops. The displacement of the plank is – (1) Lm (m M) + (2) Lm(M m) + (3) (M m) Lm + (4) LM (m M) + 12. Bullets of mass 40 g each are fired from a machine gun with a velocity of 103 m/s. If the person firing the bullets experience an average force of 200N, then the number of bullets fired per minute will be– (1) 300 (2) 600 (3) 150 (4) 75 13. If the system is released, then the acceleration of the centre of mass of the system :- (1) g 4 (2) g 2 (3) g (4) 2g 14. Initially two stable particles x and y start moving towards each other under mutual attraction. If at one time the velocities of x and y are V and 2V respectively, what will be the velocity of centre of mass of the system? (1) V (2) Zero (3) V 3 (4) V 5 15. A 2 kg body and a 3 kg body are moving along the x-axis. At a particular instant the 2 kg body has a velocity of 3 m/s and the 3 kg body has the velocity of 2 m/s. The velocity of the centre of mass at that instant is :- (1) 5 m/s (2) 1 m/s (3) 0 (4) 12m / s 5 16. Two objects of masses 200 gram and 500 gram possess velocities 10i  m/s and 3i 5 j   + m/s respectively. The velocity of their centre of mass in m/s is :- (1) 5i 25 j   − (2) 5 i 25 j 7   − (3) 25 5 i j 7   + (4) 5 25 i j 7   − MOMENTUM CONSERVATION 17. A bomb of mass 9 kg explodes into two pieces of 3kg and 6 kg. The velocity of 3 kg piece is 16 m/s. The kinetic energy of 6 kg piece is :– (1) 768 J (2) 786 J (3) 192 J (4) 687 J 18. A bomb initially at rest explodes by it self into three equal mass fragments. The velocities of two fragments are (3 ˆ i + 2 ˆ j ) m/s and (– ˆ i – 4 ˆ j ) m/s. The velocity of the third fragment is (in m/s) :- (1) 2 ˆ i + 2 ˆ j (2) 2 ˆ i – 2 ˆ j (3) –2 ˆ i + 2 ˆ j (4) –2 ˆ i – 2 ˆ j 19. A bomb of 50 Kg is fired from a cannon with a velocity 600 m/s. If the mass of the cannon is 103 kg, then its velocity will be – (1) 30 m/s (2) –30 m/s (3) 0·30 m/s (4) –0·30 m/s 20. A metal ball does not rebound when struck on a wall, whereas a rubber ball of same mass when thrown with the same velocity on the wall rebounds. From this it is inferred that – (1) Change in momentum is same in both (2) Change in momentum in rubber ball is more (3) Change in momentum in metal ball is more (4) Initial momentum of metal ball is more than that of rubber ball 21. A bomb of mass m = 1 kg thrown vertically upwards with a speed u = 100 m/s explodes into two parts after t = 5s. A fragment of mass m1 = 400 g moves downwards with a speed v1 = 25 m/s, then speed v2 and direction of another mass m2 will be :- (1) 40 m/s downwards (2) 40 m/s upwards (3) 60 m/s upwards (4) 100 m/s upwards
NEET : Physics [ 80 ] www.allendigital.in  Digital 22. A 1 kg stationary bomb is exploded in three parts having mass ratio 1 : 1 : 3. Parts having same mass move in perpendicular directions with velocity 30 m/s, then the velocity of bigger part will be :- (1) 10 2 m/s (2) 10 2 m/s (3) 15 2 m/s (4) 15 2 m/s 23. A heavy nucleus at rest breaks into two fragments which fly off with velocities 8 : 1. The ratio of radii of the fragments is :- (1) 1 : 2 (2) 1 : 4 (3) 4 : 1 (4) 2 : 1 24. A stationary particle explodes into two particles of masses m1 and m2 which move in opposite directions with velocities v1 and v2. The ratio of their kinetic energies E1/E2 is :- (1) m2/m1 (2) m1/m2 (3) 1 (4) m1v2/m2v1 25. A body of mass 4 m at rest explodes into three pieces. Two of the pieces each of mass m move with a speed  each in mutually perpendicular directions. The total kinetic energy released is :- (1) 1 2 mv 2 (2) m2 (3) 3 2 mv 2 (4) 5 2 mv 2 26. A bomb of mass 3.0 kg explodes in air into two pieces of masses 2.0 kg and 1.0 kg. The smaller mass goes at a speed of 80 m/s. The total energy imparted to the two fragments is - (1) 1.07 kJ (2) 2.14 kJ (3) 2.4 kJ (4) 4.8 kJ 27. A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 m/s. The kinetic energy of the other mass is :- (1) 524 J (2) 256 J (3) 486 J (4) 324 J 28. A bullet of mass m is fired from a gun of mass M. The recoiling gun compresses a spring of force constant k by a distance d. Then the velocity of the bullet is :- (1) kd M/ m (2) d km M (3) d kM m (4) kM d m 29. Identify the wrong statement. (1) A body can have momentum without mechanical energy (2) A body can have energy without momentum (3) The momentum is conserved in an elastic collision only. (4) Kinetic energy is not conserved in an inelastic collision COLLISION 30. A ball strikes the floor and after collision rebounds back. In this state – (1) Momentum of the ball is conserved (2) Mechanical energy of the ball is conserved (3) Momentum of ball–earth system is conserved (4) The kinetic energy of ball–earth system is conserved 31. A bullet of mass P is fired with velocity Q in a large body of mass R. The final velocity of the system will be :– (1) R P R + (2) PQ P R+ (3) (P Q) R + (4) (P ) R Q P + 32. A sphere of mass m moving with a constant velocity collides with another stationary sphere of same mass. The ratio of velocities of two spheres after collision will be, if the co- efficient of restitution is e- (1) 1 e 1 e − + (2) e 1 e 1 − + (3) 1 e 1 e + − (4) e 1 e 1 + − 33. Two elastic bodies P and Q having equal masses are moving along the same line with velocities of 16 m/s and 10 m/s respectively. Their velocities after the elastic collision will be in m/s :- (1) 0 and 25 (2) 5 and 20 (3) 10 and 16 (4) 20 and 5 34. The unit of the coefficient of restitution is – (1) m/s (2) s/m (3) m × s (4) None of the above