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 )`

Answer

D

Explanation

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