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JEE Main 2024 (6 Apr, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2024 (6 Apr, Shift 2)

Q73JEE Main 2024 · 6 APR · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

Three balls of masses 2 kg,4 kg2\text{ kg}, 4\text{ kg} and 6 kg6\text{ kg} respectively are arranged at centre of the edges of an equilateral triangle of side 2 m2\text{ m}. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be ________ kg m2\text{kg m}^2.

Numerical answer type. Work it out, then open the answer.

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Answer: 4

  1. Edge midpoints are at the inradius from the centroid: r=a23=223=13r = \frac{a}{2\sqrt3} = \frac{2}{2\sqrt3} = \frac{1}{\sqrt3} m.
  2. I=(2+4+6)r2=12×13I = (2+4+6)r^2 = 12\times\frac{1}{3}
  3. I=4I = 4 kg m2^2.
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