Q. Two identical spheres and lie on a smooth horizontal circular groove at opposite ends of a diameter. is projected along the groove and at the end of time , impinges on . If is the coefficient of restitution, then the second impact will occur after the shortest time of

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A

B

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Solution:

Let be the radius of the groove.
As and lie at opposite ends of a diameter, therefore distance covered

Speed of before impact .
Let and be velocities of and respectively after impact.

Thus the velocity of relative to after the first impact =
Let the next impact occur after seconds. This would happen when completes one round more than in time .
Distance travelled in one round =

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