JEE MAIN - Physics (2024 - 6th April Evening Shift - No. 22)
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 ________ $$\mathrm{kg} \mathrm{~m}^2$$.
Answer
4
Explanation
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Moment of inertia about c and perpendicular to the
plane is :
$$\begin{aligned} & I=2 \times\left(\frac{a}{2 \sqrt{3}}\right)^2+4 \times\left(\frac{a}{2 \sqrt{3}}\right)^2+6\left(\frac{a}{2 \sqrt{3}}\right)^2 \\\\ & I=4 \mathrm{~kg} \mathrm{~m}^2 \end{aligned}$$
Distance between centroid and midpoint of sides
$$=\frac{a}{2 \sqrt{3}}$$
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