Question

A physical pendulum consists of three equal thin bars of length l and mass m which forms an equilateral triangle as shown in figure.Find the angular frequency of small oscillations.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

The distance of the centre of mass of the pendulum from the suspension point is

$d=\frac{1}{2}sec{30}^{\circ }=\frac{1}{2}\times \frac{2}{\sqrt{2}}=\frac{1}{\sqrt{3}},$

Now,$T=2\pi \sqrt{\frac{I}{Mgd}}=\sqrt{\frac{\frac{g}{2}m{l}^2}{3mg\times \frac{1}{\sqrt{2g}}}}=\sqrt{\frac{\sqrt{31}}{2g}}$

$\Rightarrow w=\frac{2\pi }{T}=\sqrt{\frac{2g}{\sqrt{31}}}$