Question

Three point masses of $2kg$ are located at the three vertices of an equilateral triangle of side $3m$. The moment of inertia of the system of particles about an axis perpendicular to their plane and equidistant from the vertices is

• A. $9kg{m}^2$
• B. $6kg{m}^2$
• C. $2\sqrt{3}kg{m}^2$
• D. $18kg{m}^2$

Answer 1

The correct option is D $18kg{m}^2$

The axis is equidistant from the vertices .

Therefore, it passes through the circumcenter of the triangle

and is perpendicular to the plane of the rectangle.

Distance of each point mass from the axis = $\frac{l}{\sqrt{3}}$

( $l$ is the side of the triangle )

Moment of inertia = $M{r}^2$

Moment of inertia of each point mass = $2(\frac{3}{\sqrt{3}}{)}^2$

= $6$ $kg{m}^2$

By symmetry , moment of inertia of each mass is the same.

Hence , moment of inertia of the system is $I$ = $3\ast 6$ $kg{m}^2$

= $18$ $kg{m}^2$