Moment of Inertia & Radius of Gyration question from MHT CET 2025 (22 Apr, Shift 2)

Answer: (c)

1. Semicircle: $L = \pi R \Rightarrow R = \frac{L}{\pi}$.
2. $XX'$ is the diameter joining the ends. Half of a ring about its diameter keeps the same $\frac{MR^2}{2}$ form (symmetry).
3. $I = \frac{MR^2}{2} = \frac{ML^2}{2\pi^2}$
4. So the answer is (c) $\frac{ML^2}{2\pi^2}$.