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Rigid Body Dynamics: Torque — Inclined Plank MCQ

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Torque — Inclined PlankHardQuestion 30343

Question

A uniform plank (mass M, length L) rests against a smooth wall and on a rough floor. The torque due to its weight about the floor contact point is:
  1. A
    MgL sinθ
  2. B
    MgL cosθ/2
  3. C
    MgL/2
  4. D
    Mg(L/2)cosθ
    Correct

Correct answer

Mg(L/2)cosθ

Explanation

Weight Mg acts at the centre of the plank (L/2 from the floor end). Its perpendicular distance from the floor contact is (L/2)cosθ. Torque = Mg×(L/2)cosθ.

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