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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.
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Solution

The normal reaction of the wall on the ladder is N1 and that of the floor is N2
If ladder is about to slip then
According to the figure
N1=μ2N2
N2=mg+μ1N1
By torque balance equation, we get
mgcosθ2=μ1N1cosθ+N1sinθ
if μ1=0 then
mgcosθ2=N1sinθ
N1tanθ=mg2
if μ2=0 then
N1=0

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