Question

A system of two identical rods (L-shaped) of mass $m$ and length $l$ are resting on a peg $P$ as shown in the figure. IF the system is displaced in its plane by a small angle $\theta$, find the period of oscillations:

• A. $2\pi \sqrt{\frac{\sqrt{2l}}{3g}}$
• B. $2\pi \sqrt{\frac{2\sqrt{2l}}{3g}}$
• C. $2\pi \sqrt{\frac{2l}{3g}}$
• D. $3\pi \sqrt{\frac{l}{3g}}$

Answer 1

The correct option is A $2\pi \sqrt{\frac{\sqrt{2l}}{3g}}$

$T=2\pi \sqrt{\frac{I_{support}}{mg{l}_{cm}}}{I}_{support}=2\left(\frac{m{l}^2}{3}\right)=\frac{2}{3}m{l}^2{l}_{cm}=l\cos {45}^{\circ }=\frac{l}{\sqrt{2}}\Rightarrow T=2\pi \sqrt{\frac{\left(\frac{2}{3}m{l}^2\right)}{mg\left(\frac{l}{\sqrt{2}}\right)}}=2\pi \sqrt{\frac{2\sqrt{2}l}{3g}}$