Two billiard balls of the same size (radius r) and same mass are in contact on a billiard table. A third ball alsoof the same size and mass strike 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 alsoof the same size and mass strike 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 theta = 30^(@)` From conservation of linear momentum `m U = 2mvcos30^(@)ORV=(u)/(sqrt(3))` `"Now" " " E = ("relative velocity of separation")/("relative velocity of approach")` in common normal direction Hence, `e=(v)/(ucos30^(@))=(u//sqrt(3))/(usqrt(3)//2)=(2)/(3)`