Physics - Rotation Question with Solution | TestHub

Here, the rod is oscillating about an end point $O$. Hence, moment of inertia of rod about the point of oscillating is $\mathrm{I}=\frac{1}{3}\mathrm{m}{l}_0^2$ Moreover, length $l$ of the pendulum = distance from the oscillation axis to centre of mass of rod $=l_0/2$ $\therefore$ Time period of oscillation, $\begin{array}{rl}& \mathrm{T}=2\pi \sqrt{\frac{\mathrm{I}}{\mathrm{mg}l}}=2\pi \sqrt{\frac{\frac{\mathrm{l}}{3}\mathrm{m}{l}_0^2}{mg\left(\frac{l_0}{2}\right)}}\\ & \Rightarrow \mathrm{T}=2\pi \sqrt{\frac{2l_0}{3\mathrm{g}}}\\ & \end{array}$