Question

Why centre of mass taken as $R-\frac{R}{3}$ concentric?

Answer 1

Since the circles are concentric, R is the radius of bigger disc and $\frac{R}{3}$ is the radius of the smaller disc. Therefore, in order to locate the centre of mass from the main axis, we take it as $R-\frac{R}{3}$. About the concentric part, there exist two circles which have a common area along the main axis (passing through the centers of both the circles).Therefore, we locate the centre of mass of the whole system by reducing it to $R-\frac{R}{3}$.