Question

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle θ with the horizontal floor. The coefficient of friction between the wall and the ladder is μ₁ and that between the floor and the ladder is μ₂. The normal reaction of the wall on the ladder is N₁ and that of the floor is N₂. If the ladder is about to slip, then

(A) μ₁ = 0 μ₂ ≠ 0 and N₂ tanθ = mg/2

(B) μ₁  ≠ 0 μ₂ = 0 and N₁ tanθ = mg/2

(C) μ₁  ≠ 0 μ₂ ≠ 0 and N₂ = mg/1+μ₁μ₂

(D)  μ₁  = 0 μ₂  ≠ 0 and N₁ tan θ = mg/2

Answer 1

(C) μ₁  ≠ 0 μ₂ ≠ 0 and N₂ = mg/1+μ₁μ₂

(D)  μ₁  = 0 μ₂  ≠ 0 and N₁ tan θ = mg/2

Condition of translational equilibrium

Applying torque equation about corner (left) point on the floor