Question

A ladder of mass M and length L is supported in equilibrium against a smooth vertical wall and a rough horizontal surface, as shown in figure. If the angle of inclination of the rod with the horizontal, then

Determine the co-efficient of friction between ladder and horizontal surface.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

According to the free body diagram as shown in figure:-

$N_2=f;N_1=Mg$
$N_2=f$
${\tau }_{Mg}={\tau }_{N_2}$
$\left(Mg\right)\frac{L}{2}\cos \theta =N_{2}L\sin \theta$
$N_{1}L\frac{\cos \theta }{2}=fL\sin \theta$
$\frac{N_{1}L\cos \theta }{2}=\mu N_{1}L\sin \theta$
$\frac{\cos \theta }{2\sin \theta }=\mu$
$\mu =\frac{\cot \theta }{2}$