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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 option is 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×N0×f+150×2.5cos53N×5sin53=0
[taking clockwise positive and τ=rF]
2254N=0
N=56.25 N
f=56.25 N [from (1)]
Hence, options (a) and (c) are the correct answers.

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