Moment of Inertia & Radius of Gyration question from MHT CET 2024 (9 May, Shift 1)

Answer: (c)

1. Volume conserved: $\pi R^2 \cdot \frac{R}{6} = \frac{4}{3}\pi a^3 \Rightarrow a^3 = \frac{R^3}{8} \Rightarrow a = \frac{R}{2}$.
2. Disc: $I = \frac{MR^2}{2}$.
3. Sphere: $I_s = \frac{2}{5}M\frac{R^2}{4} = \frac{MR^2}{10} = \frac{I}{5}$
4. So the answer is (c) $\frac{I}{5}$.