A sphere of mass `m_(1)` in motion hits directly another sphere of mass `m_(2)` at rest and sticks to it, the total kinetic energy after collision is `2//3` of their total K.E. before collision. Find the ratio of `m_(1) : m_(2)`.

Answer

`2 : 1`

Explanation

underset(m_(1))underset(o)underset(rarr)(u)" "underset(m_(2))(o)" "underset(m_(1)m_(2))underset(oo)underset(rarr)(v)
`m_(1) m_(2) (m_(1) + m_(2))`
`COLM rArr m_(1)u + 0 = (m_(1) + m_(2))v` ….(i)
Energy equation
`((1)/(2)m u^(2)) xx (2)/(3) = (1)/(2) (m_(1) + m_(2)) v^(2)` …..(ii)
`rArr (m_(1))/(m_(2)) = 2 : 1`