Question

The two balls shwonin figure are indentical the first moving at a speed v towards right and the second staying at rest. The wall at the extreme right is fixed. Assume all collisions to be elastic. Show that the speeds of the balls remain unchanged after all the collisions have taken place.

Answer 1

1st collision: As the balls have equal mass and make elastic collision, the velocities are interchanged.
Hence, after the first collision the ball A comes to rest andk the ball B moves towards right at a speed v.
2nd collision: The ball B moving with speed v collides with teh wall and rebounds. As teh wall is rigit and may be taken to be of infinite mass, momentum conservative gives no useful result. Velocity of seperation should be equal to the velocity of approach. Hence, teh ball rebounds at teh same speed v towards left.
3rd collision: The ball B moving towards let at the speed v again collides with the ball A kept at rest. As the masses are equal and teh collision is elastic, the velocities are interchanged. Thus, the ball B comes to rest and the ball A moves towrds let at a speed v. No further collision takes place. Thus, the speeds ofthe balls remain the same as their initial values.