Q: On the flat surface of a disc of radius R, a small circular hole of radius r is made with its centre at a distance d from the centre of the disc. If mass of the whole uncut disc is M, calculate the moment of inertia of the residual disc about an axis passing through centre of the hole and perpendicular to the plane of the disc.

(a) $\displaystyle M [R^2 + 2 d^2 – \frac{r^4}{R^2}]$

(b) $\displaystyle 2 M [R^2 + 2 d^2 – \frac{r^4}{R^2}]$

(c) $\displaystyle \frac{M}{2}[R^2 + 2 d^2 – \frac{r^4}{R^2}]$

(d) $\displaystyle \frac{M}{2}[R^2 + d^2 – \frac{r^4}{R^2}]$

Ans: (c)