Two billiard balls of the same size (radius r) and same mass are in contact on a billiard table. A third ball also of the same size and mass strikes them symmetrically and remains at rest after the impact. The coefficient of restitution between the balls is

Two billiard balls of the same size (radius r) and same mass are in co

1.	Two billiard balls of the same size (radius r) and same mass are in contact on a billiard table. A third ball also of the same size and mass strikes them symmetrically and remains at rest after the impact. The coefficient of restitution between the balls is
Answer» Solution :`sin theta =(r )/(2R) = (1)/(2), THEREFORE 3 = 30^(@)` From conservation of linear momentum `m u = 2 mv = cos 30^(@) or v = (u)/(sqrt3)` 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`