Question

A uniform rod of mass $6m$ and length $6l$ is bent to make an equilateral hexagon. Its M.l. about an axis passing through the centre of mass and perpendicular to the plane to hexagon is:

• A. $5m{l}^2$
• B. $6m{l}^2$
• C. $4m{l}^2$
• D. $\frac{m{l}^2}{12}$

Answer 1

The correct option is A $5m{l}^2$

Given rod of length $6l$ is made as a hexagon of side $l$ as shown in the figure. Each side has a mass $M$.

Moment of inertia about the axis passing through the middle of a rod of length $l$ is $\frac{M{L}^2}{12}$

$M$ is mass of rod.

Hence moment of inertia of side AB of a hexagon, by parallel axis theorem = $\frac{M{L}^2}{12}+\frac{3M{L}^2}{12}=\frac{5M{L}^2}{6}$

Hence moment of inertia of all six sides = $5M{L}^2$