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
`mu = 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/ sqrt3 )/(u sqrt3/2) = 2/3`