Question

A body of mass $2\text{kg}$ is kept on a rough horizontal surface. If ${\mu }_s=0.5$ and an external force of $F=5\text{N}$ is applied on the body, find the angle of friction.
(Take $g=10{\text{m/s}}^2$)

• A. ${\tan }^{-1}\left(\frac{1}{2}\right)$
• B. ${\tan }^{-1}\left(2\right)$
• C. ${\cot }^{-1}\left(2\right)$
• D. ${\cot }^{-1}\left(\frac{1}{2}\right)$

Answer 1

The correct option is A ${\tan }^{-1}\left(\frac{1}{2}\right)$

The given situation can be shown as


The FBD of the block is

We have angle of friction as
$\tan \theta =\frac{f_s}{N}=\frac{{\mu }_{s}mg}{mg}={\mu }_s$
$\Rightarrow \theta ={\tan }^{-1}\left(0.5\right)$