Ball 1 collides with an another identical ball 2 at rest as shown in figure. For what value of coefficient of restitution e, the velocity of ball 2 becomes two times that of ball I after collision? 

Options

A. `1/3`
B. `1/2`
C. `1/4`
D. `1/6`

Answer

A

Explanation

Let u be the initial velocity of ball 1. Then , after collision
`v_1 = ((1 - e)/(2)) u and v_2 = ((1 +e)/(2)) u :. (v_2)/(v_1) = (1 + e)/(1 - e)`
But `v_2 = 2v_1` (given ) `:. 2 = (1 + e)/(1 - e)`
On solving, we get `e = 1/3`.