Consider a badminton racket with length scales as shown in the figure. If the mass of the linear and circular portions of the badminton racket are same $(M)$ and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, $\frac{r}{2}$ distance from the end $A$ of the handle will be $\_\_\_\_$ $\mathrm{Mr}^2$.