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), " " therefore theta = 30^(@)`
From conservation of linear momentum
`m u = 2mv 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)`