Q: From a semi-circular disc of mass M and radius R_{2} , a semi – circular disc of radius R_{1} is removed as shown in the figure. If the mass of original uncut disc is M, find the moment of inertia of residual disc about an axis passing through centre O and perpendicular to the plane of the disc.

(a) $\displaystyle \frac{M}{2 R_2^2}(R_2^4 – R_1^4)$

(b) $\displaystyle \frac{M}{R_2^2}(R_2^4 – R_1^4)$

(c) $\displaystyle \frac{M}{ R_2^2}(\frac{R_2^4}{4} – R_1^4)$

(d) $\displaystyle \frac{M}{ R_2^2}(R_2^4 – \frac{R_1^4}{4})$

Ans: (a)