Two equal spheres `A` and `B` lie on a smooth horizontal circular groove at opposite ends of a diameter. At time `t = 0`, A is projected along the groove and it first impinges 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. The second impact will occur after time T
B. The second impact will occur after time `(2T)/(e )`
C. The second impact will occur after time 2T
D. None of these

Answer

B

Explanation

Let `V_2`: velocity of separation and `V_1` = and velocity of approach
`implies T = (pi R)/(V_1) and V_2 = eV_1 " " implies 2^(nd)` collision occur after time = `(2 pi R)/(V_2) implies`
`t = (2 pi R)/(eV_1) = (2T)/(e )`.