Moment of Inertia & Radius of Gyration question from MHT CET 2024 (16 May, Shift 2)

Answer: (c)

1. The mass at the vertex lies on the axis, so it contributes nothing.
2. The other two masses are at distance equal to the triangle's height $h = \frac{\sqrt{3}}{2}L$ from the axis.
3. $I = 2m\left(\frac{\sqrt{3}L}{2}\right)^2 = \frac{3mL^2}{2}$
4. So the answer is (c) $\frac{3mL^2}{2}$.