Moment of Inertia & Radius of Gyration question from MHT CET 2024 (10 May, Shift 1)

Answer: (d)

1. Sphere: $I = \frac{2}{5}MR^2$ (mass unchanged on recasting).
2. Disc about an axis through its edge, perpendicular to plane: $I = \frac{Mr^2}{2} + Mr^2 = \frac{3}{2}Mr^2$.
3. $\frac{3}{2}Mr^2 = \frac{2}{5}MR^2 \Rightarrow r^2 = \frac{4}{15}R^2$
4. So the answer is (d) $\frac{r}{R} = \frac{2}{\sqrt{15}}$.