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NTA Abhyas JEE Main2020PhysicsRotational MotionPractice

Four holes of radius R are cut from a thin square plate of side 4 R and mass M . The moment of inertia of the remaining portion about the x -axis is

Options

  1. Aπ 12 M R 2
  2. B4 3 - π 4 M R 2
  3. C4 3 - π 6 M R 2
  4. D8 3 - 10 π 16 M R 2

Correct answer

D. 8 3 - 10 π 16 M R 2

Step-by-step solution

If M mass of the square plate before cutting the holes, then mass of portion of each hole, m = M 16 R 2 × π R 2 = π 16 M ∴ Moment of inertia of remaining portion I = I s q u a r e - 4 I h o l e = M 12 16 R 2 + 16 R 2 - 4 m R 2 2 + m 2 R 2 = M 12 × 32 R 2 - 10 m R 2 = 8 3 M R 2 - 10 π 16 M R 2 = 8 3 - 10 π 16 M R 2

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