A uniform metal disc of radius R is taken and out of it a disc of diameter R is cut off from the end. The centre of mass of the remaining part will be

 

$\begin{array}{l}C\text{entre of mass of the uncut disc is at O.}\\ {\text{Let the position of centre of mass of the remaining disc is C}}_1\text{ and }\\ {\text{the positon of centre of mass of the removed disc is C}}_2.\\ Applying\text{ law of moments about O}\\ \text{s}\left(\text{mass of remaining disc}\right)=\frac{R}{2}\left(mass\text{ of removed disc}\right)\\ s\left[\sigma \left(\pi R^2-\frac{\pi R^2}{4}\right)\right]=\frac{R}{2}\left[\sigma \frac{\pi R^2}{4}\right]\\ s=\frac{R}{6}\end{array}$