Moment of Inertia & Radius of Gyration question from MHT CET 2025 (22 Apr, Shift 1)

Answer: (c)

1. $I_s = \frac{2}{5}MR_s^2$ and $I_h = \frac{2}{3}MR_h^2$.
2. Same mass and same material means the thin hollow sphere must be much larger: $R_h > R_s$.
3. Also $\frac{2}{3} > \frac{2}{5}$, and the hollow sphere's mass is all at the largest radius, so $I_h > I_s$.
4. So the answer is (c) $I_h > I_s$.