Question

A circular disc of radius ${}^{\prime }{R}^{\prime }$ and mass ${}^{\prime }{m}^{\prime }$ is hinged at the centre about horizontal axis. A particle of same mass is attached at the top of the disc. Now the system is released. Calculate the angular velocity of the disc when the particle reaches bottom.

• A. $\sqrt{\frac{8g}{3R}}$
• B. $\sqrt{\frac{7g}{3R}}$
• C. $\sqrt{\frac{2g}{R}}$
• D. $\sqrt{\frac{5g}{3R}}$

Answer 1

The correct option is A $\sqrt{\frac{8g}{3R}}$

Let $\omega$ be angular velocitywhen mass reaches the bottom.
Now from conservation of angular momentum,

$mg\left(2R\right)+0=\frac{1}{2}I{\omega }^2$
$2mgR=\frac{1}{2}(\frac{m{R}^2}{2}+m{R}^2){\omega }^2$
$\omega =\sqrt{\frac{8g}{3R}}$