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JEE Main 2024 (27 Jan, Shift 1) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2024 (27 Jan, Shift 1)

Q63JEE Main 2024 · 27 JAN · SHIFT 1Easy

Moment of Inertia & Radius of Gyration

Four particles each of mass 1 kg1\text{ kg} are placed at four corners of a square of side 2 m2\text{ m}. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is _____ kg m2\text{kg m}^{2}.

Figure

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

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Answer: 16

  1. The mass at the chosen vertex is on the axis. Two adjacent masses are at 22 m and the opposite one is at 222\sqrt{2} m.
  2. I=1(2)2+1(2)2+1(22)2=4+4+8I = 1(2)^2 + 1(2)^2 + 1(2\sqrt{2})^2 = 4 + 4 + 8
  3. I=16 kg m2I = 16\ \text{kg m}^2
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