Question

A system of particles is shown in figure. Point mass particles of same mass $m$ are present at each corner of the hexagon whose each side is equal to $a$. Find the $MOI$ about an axis passing through its $COM$ and perpendicular to its plane.

• A. $6m{a}^2$
• B. $3m{a}^2$
• C. $4m{a}^2$
• D. $2m{a}^2$

Answer 1

The correct option is A $6m{a}^2$

As we can see from symmetry, $COM$ of the particles will be at the center of the hexagon at point $\text{O}$.


As we can see from the figure, distance of every particle from the $COM$ will be $a$.

Hence, $MOI$ about an axis passing through point $\text{O}$ is,
$I=I_1+I_2+I_3+I_4+I_5+I_6$
$I=m{a}^2+m{a}^2+m{a}^2+m{a}^2+m{a}^2+m{a}^2$
$I=6m{a}^2$