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MHT CET 2024 (11 May, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from MHT CET 2024 (11 May, Shift 2)

Q86MHT CET 2024 · 11 MAY · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

Four thin metal rods each of mass ' MM ' and length ' LL ', are welded end to end to form a square. The moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane is

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Answer: (d)

  1. Each rod's centre is L2\frac{L}{2} from the square's centre.
  2. One rod: ML212+M(L2)2=ML23\frac{ML^2}{12} + M\left(\frac{L}{2}\right)^2 = \frac{ML^2}{3}
  3. Four rods: I=4ML23I = \frac{4ML^2}{3}
  4. So the answer is (d) 4ML23\frac{4ML^2}{3}.
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