A sphere `A` impinges directly on an identical sphere `B` at rest. If coefficient of restitution is `e` , the ratio of velocities of `A` and `B` after collision is

Options

A. `(1 - e)/(1 + e)`
B. `(1 + e)/(1 - e)`
C. `(e )/(1 + e)`
D. `(2e)/(1 + e)`

Answer

A

Explanation

`m u = mv_(1) + mv_(2) rArr v_(1) + v_(2) = u` (i)
`v_(1) - v_(2) = -e(u_(1) - u_(2))`
`v_(1) - v_(2) = -eu` (ii)
Solving the above equation , we get
`v_(1) = ((1 - e)u)/(2) , v_(2) = ((1 + e)u)/(2)`
`(v_(1))/(v_(2)) = (1 - e)/(1 + e)`