Q 11-06-151JEE MainJEE Main 2021 (24 Feb, Shift 2)Medium
A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is ______ $\times10^{-1}$ kg m$^2$.
Numerical value type. Enter your answer.
Answer: 8
Each side has mass $m = 1$ kg and length $l = 0.4$ m. The centre of each side is at distance $\frac{\sqrt3}{2}l$ from the centre of the hexagon. By the parallel axis theorem, for one side:
$$I_1 = \frac{ml^2}{12} + m\left(\frac{\sqrt3 l}{2}\right)^2 = ml^2\left(\frac{1}{12} + \frac34\right) = \frac56ml^2$$
$$I = 6\times\frac56\times1\times(0.4)^2 = 0.8\ \text{kg m}^2 = 8\times10^{-1}\ \text{kg m}^2$$
Solution by Sreeraj P, M.Sc Physics