Moment of Inertia & Radius of Gyration question from NEET 1999 (AIPMT)

Answer: (d)

1. About a diameter (in the plane): $I_d = \frac{1}{4}MR^2$ (perpendicular axis theorem: $2I_d = \frac{1}{2}MR^2$).
2. Tangent in the plane is parallel to a diameter at $d = R$: $I = \frac{1}{4}MR^2 + MR^2$.
3. So the answer is (d) $\frac{5}{4}MR^2$.