Question

A thin uniform rod of length l is pivoted at its upper end. It is free to swing in a vertical plane. Its time period for oscillations of small amplitude is

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

Answer 1

The correct option is B

$2\pi \sqrt{\frac{2l}{3g}}$

$T=2\pi \sqrt{\frac{I}{C}}=2\pi \sqrt{\frac{\frac{m{l}^2}{3}}{mg\frac{l}{2}}}$

Here C represents the position of centre of mass

$T=2\pi \sqrt{\frac{2l}{3g}}$