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Question 30367
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Rigid Body Dynamics: JEE — Torque Equilibrium MCQ

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JEE — Torque EquilibriumHardQuestion 30367

Question

A uniform ladder (mass M, length L) leans against a smooth wall, foot on rough floor. For equilibrium, the torque equation about the base gives the wall reaction N_w as:
  1. A
    MgL cosθ/(2 sinθ)
  2. B
    Mg tanθ/2
  3. C
    Mg/(2 tanθ)
    Correct
  4. D
    Mg cosθ/2

Correct answer

Mg/(2 tanθ)

Explanation

Taking torques about the base: N_w × L sinθ = Mg × (L/2) cosθ. N_w = Mg cosθ/(2 sinθ) = Mg/(2 tanθ).

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