Moment of Inertia & Radius of Gyration question from NEET 2000 (AIPMT)

Answer: (b)

1. For a triangular lamina about one side, $I = \frac{Mh^2}{6}$, where $h$ is the perpendicular distance of the opposite vertex from that side.
2. About $AB$ ($I_1$): $h = BC = 3 \Rightarrow I_1 = \frac{9M}{6} = 1.5M$
3. About $AC$ ($I_2$): $h = \frac{3 \times 4}{5} = 2.4 \Rightarrow I_2 = \frac{5.76M}{6} = 0.96M$
4. About $BC$ ($I_3$): $h = AB = 4 \Rightarrow I_3 = \frac{16M}{6} \approx 2.67M$
5. So $I_3 > I_1 > I_2$: options (a), (c) and (d) hold, and (b) $I_2 > I_1$ does not.