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Question

A uniform ladder of length L.rests against frictionless wall. The floor is rough and the coefficient of static friction between the floor and ladder is μ. When the ladder is positioned at angle θ , as shown in the accompanying, it is just about to slip.What is θ?
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A
cosθ=μ
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B
tanθ=2μ
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C
tanθ=12μ
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D
sinθ=1μ
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Solution

The correct option is C tanθ=12μ

Given,

Coefficient of friction =μ


Forces in vertical direction, N1=mg

Forces in horizontal direction, N2=μmg

Moment at point A, take clockwise direction positive.

N2LsinθmgL2cosθ=0

μmgLsinθmgL2cosθ=0

tanθ=12μ


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