Two sphere `A` and `B` of equal masses lie on the smooth horizontal circular groove at opposite ends of diameter and at the end of time 't','A' impings on 'B' . If 'e' is the coefficient of restitution, the second impinge will occur after a time

Options

A. `(2t)/( e)`
B. `(t)/( e)`
C. `(pi t)/( e)`
D. `(2 pi t)/( e)`

Answer

A

Explanation

`t = (pir)/(u_(1)),e = (v_(2)-v_(1))/(u_(1)),v_(2) -v_(1) = eu_(1)`
and second impact, `t_(1)=(2pir)/(v_(2)-v_(1)) =(2pi r)/(eu_(1)) =(2t)/(e)`.