Question

A block kept on a rough surface starts sliding when the inclination of the surface is '$\theta$' with respect to the horizontal. The coefficient of static friction between the block and the surface is:

• A. $\sin \theta$
• B. $\tan \theta$
• C. $\cos \theta$
• D. $\sec \theta$

Answer 1

Answer: (B)

$\tan \theta$

Free body diagram for the given scenario is shown in the figure.

Forces normal to the plane are balanced as the block cannot move normal to the plane.

$N=mg\cos \theta ..............\left(i\right)$

When the body just begins to slide, forces parallel to the plane are balanced.

$F_r=mg\sin \theta ..............\left(ii\right)$

Frictional force acting when the body just begins to slide is given by:

$F_r=\mu N..............\left(iii\right)$

Substituting (i) & (iii) in (ii), we get

$\mu mg\cos \theta =mg\sin \theta$

$\mu =\tan \theta$