In the figure as shown, a triangular portion is cut from a circular disc of radius $R$. The distance

Question

In the figure as shown, a triangular portion is cut from a circular disc of radius $R$. The distance of centre of mass of the remainder from the centre of the disc is :

Professor PC Thomas Classes · Answer

Mass of remaining portion $=\left(\pi R^2-\frac{R^z}{4}ight) e$
Mass of triangular portion $=\frac{R^2}{4} e$
$$
\begin{aligned}
& R^2\left(\pi-\frac{1}{4}ight) e x=\frac{R^2}{4} e \frac{2}{3}\left(\frac{R}{2}ight) \
& \Rightarrow x=\frac{R}{3(4 \pi-1)}
\end{aligned}
$$