Physics - Rotation Question with Solution | TestHub

Equilateral triangle (mass m, side a) about the in-plane median axis through the apex: $I=\frac{m{a}^2}{24}$

Regular hexagon (side a) about the in-plane axis through centre: $I_{hex}=\frac{5M{a}^2}{24}$ with $M=6m$ (6 such triangles of same material).

$I_{hex}=\frac{5\times 6m{a}^2}{24}=30\frac{m{a}^2}{24}=30I=10\alpha I\Rightarrow \alpha =3$