Two equal sphere `A and b` lie on a smooth horizontal circle groove at opposite ends of a diameter. At time `t= 0,A` is projected along the groove and tis first implings on`B` at time `t = T_(1) and again at time `t = T_(2). If `e` is the coefficient of restitution, the ratio `T_(2)//T_(1)` is

Options

A. `(2)/( e)`
B. `((2 + e))/(2)`
C. `(2(e + 1))/( e)`
D. `(2 + e)/( e)`

Explanation

`T_(1) = (pi R)/(u_(1))` (1)

Time taken to collide `A and B` again:
`T_(2) - T_(1) = (2 pi R)/(v_(2) - v_(1)) implies T_(2) - T_(1) = (2 pi R)/(eu_(1))` (2)
(2) + (1) `implies (T_(2))/(T_(1)) = (2 + e)/( e)`