Question

A block of mass $m$ rests on a rough inclined plane. The coefficient of friction between the surface and the block is $\mu$. At what angle of inclination $\theta$ of the plane to the horizontal will the block just start to slide down the plane?

• A. $\theta$ $=tan^{-1}$ $\mu$
• B. $\theta$ $=cos^{-1}$ $\mu$
• C. $\theta$ $=sin^{-1}$ $\mu$
• D. $\theta$ $=sec^{-1}$ $\mu$

Answer 1

Answer: (A)

The various forces acting on the block are as shown in the figure.
From figure
$mg$ $sin \,\theta=f $ $ \quad\ldots\left(i\right)$
$mg$ $cos \, \theta=N$ $\quad\ldots\left(ii\right)
$
Divide (i) by (ii), we get
$tan \,\theta$ $=\frac{f}{N}$ $=\frac{\mu\,N}{N}$ or $\theta$ $=tan^{-1}$ $ \left(\mu\right)$