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Question

# A uniform ladder of mass 15 kg leans against a smooth vertical wall making an angle of 37∘ with it. The other end rests on a rough horizontal floor. Which of the following is/are correct?

A
Normal force by the floor on the ladder is 150 N.
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B
Normal force by the floor on the ladder is 170 N.
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C
Frictional force by the floor on the ladder is 56.25 N.
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D
Frictional force by the floor on the ladder is 60 N.
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Solution

## The correct options are A Normal force by the floor on the ladder is 150 N. C Frictional force by the floor on the ladder is 56.25 N.Let us suppose normal force and frictional force by the floor on the ladder are N and f respectively as shown in the figure. For translational equilibrium along vertical, ∑Fy=0 ⇒ Normal force (N) = Weight of the ladder (mg) ∴N=15×10=150 N For translational equilibrium along horizontal, ∑Fx=0 ⇒f=N′ ... (1) For rotational equilibrium about point A, ∑τ=0 ⇒0×N−0×f+150×2.5cos53∘−N′×5sin53∘=0 [taking clockwise positive and τ=r⊥F] ⇒225−4N′=0 ⇒N′=56.25 N ⇒f=56.25 N [from (1)] Hence, options (a) and (c) are the correct answers.

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