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 $\mu$. When the ladder is positioned at angle $\theta$ , as shown in the accompanying, it is just about to slip.What is $\theta$?

• A. $cos\theta =\mu$
• B. $tan\theta =2\mu$
• C. $tan\theta =\frac{1}{2\mu }$
• D. $sin\theta =\frac{1}{\mu }$

Answer 1

The correct option is C $tan\theta =\frac{1}{2\mu }$

Given,

Coefficient of friction $=\mu$

Forces in vertical direction, $N_1=mg$

Forces in horizontal direction, $N_2=\mu mg$

Moment at point A, take clockwise direction positive.

$N_{2}L\sin \theta -mg\frac{L}{2}\cos \theta =0$

$\mu mgL\sin \theta -mg\frac{L}{2}\cos \theta =0$

$\tan \theta =\frac{1}{2\mu }$