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JEE Main 2022 (30 Jun, Shift 1) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2022 (30 Jun, Shift 1)

Q113JEE Main 2022 · 30 JUN · SHIFT 1Medium

Moment of Inertia & Radius of Gyration

Four particles with a mass of 1 kg, 2 kg, 3 kg and 4 kg are situated at the corners of a square with side 1 m (as shown in the figure). The moment of inertia of the system, about an axis passing through the point O and perpendicular to the plane of the square, is ______________ kg m2.

Figure

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

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Answer: 5

  1. Each mass is at distance 12 m\frac{1}{\sqrt{2}}\text{ m} from O (half the diagonal), so r2=12 m2r^2 = \frac{1}{2}\text{ m}^2.
  2. I=∑mr2=(1+2+3+4)×12I = \sum m r^2 = (1+2+3+4) \times \frac{1}{2}
  3. I=5 kg m2I = 5\text{ kg m}^2
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