In the previous problem , sphere `A` is moving with speed `u_(1)` and sphere `B` with speed `u_(2)` in opposite direction. After the collision , sphere `A` comes to rest , then `u_(1)//u_(2)` is

Options

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

Answer

B

Explanation

`m u_(1) - m u_(2) = mv_(1) + mv_(2)` (i)
`v_(1) - v_(2) = -e (u_(1) - u_(2))` [use velocities with sign]
`v_(1) - v_(2) = -e{u_(1) - u_(2)}` (ii)
`v_(1) + v_(2) = u_(1) - u_(2)` (i)
`v_(1) - v_(2) = -e(u_(1) + u_(2))` (ii)
Given , `v_(1) = 0` , by solving , we get
`(u_(1))/(u_(2)) = (1 + e)/(1 - e)`