Two identical billiard balls are in contact on a table. A third identical ball strikes them symmetrically and comes to rest after impact. The coefficient of restitution is :

Options

A. `(2)/(3)`
B. `(1)/(3)`
C. `(1)/(6)`
D. `(sqrt3)/(2)`

Answer

A

Explanation

sin `theta = (r)/(2r) = (1)/(2) implies theta = 30^(@) `
mu = 2mv cos `30^(@)` or v = `(u)/(sqrt3)`
Now e = `(v)/(u cos 30^(@)) = (u // sqrt3)/(u sqrt3 //2) = (2)/(3)`