Question

A box is lying on an inclined plane what is the coefficient of static friction if the box starts sliding when an angle of inclination is $60°$?

• A. $1.173$
• B. $1.732$
• C. $2.732$
• D. $1.677$

Answer 1

The correct option is B

$1.732$

Step 1. Given data

Angle of inclination$=60°$

Step 2. Finding the value of the coefficient of static friction, $\mu$

The tangential component of force $=mg\sin 60°$

The normal component of force, $N=mg\cos 60°$

Frictional force $=\mu N$ [Where, $g$ is acceleration due to gravity]

$=\mu mg\cos 60°$

Just before sliding

The tangential component of force = Frictional force

$mg\sin 60°=\mu mg\cos 60°$

$\mu =\tan 60°$

$\mu =\sqrt{3}$

$\mu =1.732$

Hence, the correct option is $\left(B\right)$.