A sphere `A` of mass `m` moving with a velocity hits another stationary sphere `B` of same mass. If the ratio of the velocity of the sphere after collision is `(v_(A))/(v_(B)) = (1 - e)/(1 + e)` where `e` is the coefficient of restitution, what is the initial
velocity of sphere `A` with which it strikes?

Options

A. `V_(A) + V_(B)`
B. `V_(A) - V_(B)`
C. `V_(B) - V_(A)`
D. `(V_(B) + V_(A))/2`

Answer

`(1)`

Explanation

`(v_(A)/(v_(B)) = (1-e)/(1 + e) Rightarrow e = (v_(B) - v_(A))/(v_(A) + v_(B)) ---(1)`
we have `e = (v_(2) - v_(1))/(u_(1) - u_(2)) = (v_(B) -v_(A))/(u_(A) - 0) ---(2)`
form (1) and (2) , `u_(A) = ?`