A uniform bar of length $6a$ and mass $8m$ lies on a smooth horizontal table. Two point masses $m$ and $2m$ moving in the same horizontal plane with speeds $2\upsilon$ and $\upsilon ,$ respectively strike the bar as shown in the figure and stick to it after collision. Denoting angular velocity (about the centre of mass), total energy and velocity of the centre of mass by $\omega ,$ E and $V_c$ respectively, we have after collision,