Question

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

• A. $\theta =ta{n}^{-1}\mu$
• B. $\theta =co{s}^{-1}\mu$
• C. $\theta =si{n}^{-1}\mu$
• D. $\theta =se{c}^{-1}\mu$

Answer 1

The correct option is A $\theta =ta{n}^{-1}\mu$

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