Three balls of masses 2 kg, 4 kg, and 6 kg respectively are arranged at the center of the edges of an equilateral triangle of side 2 m. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of the triangle w

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Solution

Q.
Three balls of masses 2 kg, 4 kg, and 6 kg respectively are arranged at the center of the edges of an equilateral triangle of side 2 m. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of the triangle will be ____ kg $m^{2}$ . [2024]

Ans.
(4)

$r \cos 30 ° = \frac{1}{2} \Rightarrow r = \frac{1}{\sqrt{3}}$

$I = m_{1} r^{2} + m_{2} r^{2} + m_{3} r^{2}$

$I = (2 + 4 + 6) r^{2} = 12 \times \frac{1}{3} = 4 \Rightarrow I = 4 {kg-m}^{2}$

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