Three balls of masses `m_(1), m_(2)` and `m_(3)` are lying in a straight line. The first ball is moved with a certain velocity so that it strikes the second ball directly and itself comes to rest. The second ball collides with the third and is itself reduced to rest. If `e` is the coefficient of restitution for each ball, write down the relation of `m_(3)` in terms of `m_(1)` and `m_(2)`.

Explanation

After first impact `v_(1)=0`
`implies ((m_(1)-em_(2))/(m_(1)+m_(2)))u_(1)=0impliesm_(1)=em_(2)`……….i

After second impact `v_(3)=0`
`implies ((m_(1)-em_(3))/(m_(1)+m_(3)))v_(2)=0impliesm_(2)=em_(3)`………ii
From i and ii `m_(2)^(2)=m_(1)m_(3)`