Three balls of masses $2 \mathrm{~kg}, 4 \mathrm{~kg}$ and $6 \mathrm{~kg}$ respectively are arranged at…
Three balls of masses $2 \mathrm{~kg}, 4 \mathrm{~kg}$ and $6 \mathrm{~kg}$ respectively are arranged at centre of the edges of an equilateral triangle of side $2 \mathrm{~m}$. The moment of intertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be _______ $\mathrm{kg} \mathrm{m}^2$.
Solution
Moment of inertia about $\mathrm{C}$ and perpendicular to the plane is :
$\begin{aligned}
\mathrm{I} & =\mathrm{r}^2[2+4+6] \\
& =\frac{1}{3} \times 12 \\
\mathrm{I} & =4 \mathrm{~kg}-\mathrm{m}^2
\end{aligned}$
