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

Answer

D

Explanation

`T_(1)=(piR)/u_(1)`
`(v_(2)-v_(1))/u_(1)=eimpliesv_(2)-v_(1)-eu_1`

Time taken to collide `A` and `B` again is
`T_(2)-T_(1)=(2piR)/(v_(2)-v_(1)) implies T_(2)-T_(1)=(2piR)/(eu_(1))`………..ii
Dividing ii by i, we get `T_(2)/T_(1)=(2+e)/e`