A thin uniform bar of length L and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal plane…

A thin uniform bar of length L and mass $\displaystyle 8$ m lies on a smooth horizontal table. Two point masses m and $\displaystyle 2$ m are moving in the same horizontal plane from opposite sides of the bar with speeds $\displaystyle 2 v$ and $\displaystyle v$ respectively. The masses stick to the bar after collision at a distance $\displaystyle \frac{\mathrm{L}}{3}$ and $\displaystyle \frac{\mathrm{L}}{6}$ respectively from the centre of the bar. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be :