A thin uniform bar of length L and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m moving in the same horizontal plane from opposite sides of the bar with speeds 2 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: [Figure] (1) $\frac { \mathrm { v } } { 6 \mathrm {~L} }$ (2) $\frac { 6 \mathrm { v } } { 5 \mathrm {~L} }$ (3) $\frac { 3 \mathrm { v } } { 5 \mathrm {~L} }$ (4) $\frac { \mathrm { v } } { 5 \mathrm {~L} }$
A thin uniform bar of length L and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m moving in the same horizontal plane from opposite sides of the bar with speeds 2 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:\\
\includegraphics[max width=\textwidth, alt={}, center]{1350fc77-f386-413d-b099-6e647954663e-02_332_741_1418_267}\\
(1) $\frac { \mathrm { v } } { 6 \mathrm {~L} }$\\
(2) $\frac { 6 \mathrm { v } } { 5 \mathrm {~L} }$\\
(3) $\frac { 3 \mathrm { v } } { 5 \mathrm {~L} }$\\
(4) $\frac { \mathrm { v } } { 5 \mathrm {~L} }$