Two billiard balls of same size and mass are in contact on a billiard table. A third ball of same mass and size strikes them symmetrically and remains at rest after the impact. Find the coefficient of restitution between the balls?

Explanation

`sin theta = ( r)/(2r) = (1)/(2)` ,
`:. theta = 30^@`
From conservation of linear momentum
`m u = 2 mv cos 30^@` or `v = (u)/(sqrt(3))`
Now `e = ("relative velocity of separation")/("relative velocity of approach")`
in common normal direction.
Hence, `e = (v)/(u cos 30^@) = (u//sqrt(3))/(u sqrt(3)//2) = (2)/(3)`.