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 cofficient 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_(A) + v_(B)))/(2)`

Answer

B

Explanation

`(v_(A))/(v_(B))=(1-e)/(1+e)`
`(v_(A))/(V_(B))-1(1-e)/(1+e)-1`
or `v+(B) -v_(A) =(2e)/(1+e) .ve`
But `e=(v_(B)-v_(A))/(u)`
or `u=(2ev_(B))/(e(1+e)) rArr u+eu=2v_(B)`
or `u+(v_(B)-v_(A))=2v_(B)rArr u=v_(A)+V_(B)`.