JEE Main 2018 — Rotational Motion Question with Solution

A thin uniform bar of length $\mathrm{L}$ and mass $8\mathrm{m}$ lies on a smooth horizontal table. Two point masses $\mathrm{m}$ and $2\mathrm{m}$ moving in the same horizontal plane from opposite sides of the bar with speeds $2\mathrm{v}$ and $v$ respectively. The masses stick to the bar after collision at a distance $\frac{\mathrm{L}}{3}$ and $\frac{\mathrm{L}}{6}$ 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: