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

A

Explanation

`(v_(A))/(v_(B)) = (1-e)/(1+e) rArr 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)
from (1) and (2), `u_(A) = ?`.