Two identical balls of equal masses A and B, are lying on a smooth surface as shown in the figure. Ball A hits the ball B (which is at rest) with a velocity `v=16ms^-1`. What should be the minimum value of coefficient of restitution `e` between A and B so that B just reaches the highest point of inclined plane? `(g=10ms^-2)`

Options

A. `2/3`
B. `1/4`
C. `1/2`
D. `1/3`

Answer

B

Explanation

`v=16m//s`

Let velocity of `B` after collision be `v_(2)` and that of `A` be `v_(1)`. Then
`v-=sqrt(2gh)=sqrt(2xx10xx5)=10m//s`
`mv_(1)+mv_(2)=mv`
`v_(1)+10=16impliesv_(1)=6m//s`
`e=(v_(2)-v_(1))/v=(10-6)/16=1/4`