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_(A)+V_(B)))/2`

Answer

1

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) V_(B)`
But `e=(V_(B)-V_(A))/u`
so `u=(2eV_(B))/(e(1+e))`
or `u+eu=2V_(B)`
`u+(V_(B)-V_(A))=2V_(B)`
`u=V_(A)+V_(B)`