Question

A semicircular disc of mass $M$ and radius $R$ shown in figure $OA$ is initially vertical. Disc is released from this position when $OA$ becomes horizontal, then angular velocity of disc is

Answer 1

wall$=\Delta K$

$\begin{array}{c}\Rightarrow mg\left(R-\frac{4R}{2\pi }\right)=\frac{1}{2}\left(hing\right)w^2\\ \Rightarrow mgR\left(1-\frac{4}{3\pi }\right)=\frac{1}{2}\times \frac{3m{R}^2}{2}{w}^2\\ \Rightarrow \frac{4g}{3R}\left(1-\frac{4}{3\pi }\right)=w^2\\ Hence,\\ \Rightarrow w=\sqrt{\frac{4g}{3R}\left(1-\frac{4}{3\pi }\right)}\end{array}$