Moment of Inertia & Radius of Gyration question from MHT CET 2020 (16 Oct, Shift 2)

Answer: (d)

1. Ring, tangent perpendicular to plane: $MR^2 + MR^2 = 2MR^2 \Rightarrow K_r = \sqrt{2}R$.
2. Disc, tangent perpendicular to plane: $\frac{1}{2}MR^2 + MR^2 = \frac{3}{2}MR^2 \Rightarrow K_d = \sqrt{\frac{3}{2}}R$.
3. $\frac{K_r}{K_d} = \sqrt{\frac{2}{3/2}} = \frac{2}{\sqrt{3}}$
4. So the answer is (d) $\frac{2}{\sqrt{3}}$.