Question

From a uniform disc of radius $R$, a small disc of radius $\frac{R}{2}$ is cut and removed as shown in the diagram. Find the center of mass of the remaining portion of the disc.

Answer 1

let the com of the original disebe at the origin
Bow let the com of small disc lie to the right
com of disc =at its centre
$\therefore$ com $=\frac{R}{2}$ of small disc
let the com of large disc be situated at $c$cm then com of large disc $\Rightarrow x$
Now area of entire sheet $\Rightarrow \pi R^2;mass/area=\frac{m}{\pi R^2}$