Question 404: Centre of Mass and Rotational Motion

Question

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 inertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be ________ $$\mathrm{kg} \mathrm{~m}^2$$.

Accepted Answer

Moment of inertia about c and perpendicular to the
plane is :
$$\begin{aligned}
& I=2 	imes\left(\frac{a}{2 \sqrt{3}}ight)^2+4 	imes\left(\frac{a}{2 \sqrt{3}}ight)^2+6\left(\frac{a}{2 \sqrt{3}}ight)^2 \\
& I=4 \mathrm{~kg} \mathrm{~m}^2
\end{aligned}$$
Distance between centroid and midpoint of sides
$$=\frac{a}{2 \sqrt{3}}$$

Centre of Mass and Rotational Motion

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