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MHT CET202519 Apr 2025Morning ShiftPhysicsRotational MotionActual

Four particles each of mass M are placed at the corners of a square of side L . The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

Options

  1. AL
  2. BL 2
  3. CL 4
  4. DL 2

Correct answer

D. L 2

Step-by-step solution

The system consists of four particles of mass M arranged at the corners of a square of side L . The rotation axis is perpendicular to the square's plane and passes through its center. The distance r from each corner to the center is half the diagonal length. The diagonal is L 2 , so r = L/ 2 . The moment of inertia for one particle about this axis is Mr^2 = M(L^2 / 2) = ML^2 / 2 . For four identical particles, the total moment of inertia is I_ total = 4(ML^2 / 2) = 2ML^2 . The total mass is M_ total = 4M . The radi

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