A plank AB of length l is gently released on a knife edge at 0 as shown in the figure. If $AO$is made $\raisebox{1ex}{$l$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$, the angular acceleration of the plank just after it is released is 

Mass of segment $AO,m_1=\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

Mass of segment $BO,m_2=\raisebox{1ex}{$3m$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

M = Net moment about $O=\frac{3mg}{4}\times \frac{3l}{8}-\frac{mg}{4}\times \raisebox{1ex}{$l$}\!\left/ \!\raisebox{-1ex}{$8$}\right.$

$=\frac{1}{4}mgl$

$I_0=\frac{1}{3}\left(\frac{m}{4}\right){\left(\frac{l}{4}\right)}^2+\frac{1}{3}\left(\frac{3m}{4}\right){\left(\frac{3l}{4}\right)}^2=\frac{7}{48}m{l}^2$

$\therefore$ Angular acceleration, $\alpha =\frac{M}{I_0}=\frac{\frac{1}{4}mgl}{\frac{7}{48}m{l}^2}=\frac{12}{7}\frac{\text{g}}{l}$