Question

The coefficient of friction between two surfaces is 0.2. The angle of friction is

• A. ${\sin }^{-1}(0.2)$
• B. ${\cos }^{-1}(0.2)$
• C. ${\tan }^{-1}(0.1)$
• D. ${\cot }^{-1}(5)$

Answer 1

Answer: (D)

Angle of sliding or repose is the angle that an inclined plane makes with the horizontal when a body placed on it just starts sliding down.

$f_{\max }=\mu N$
$N=mg\cos \theta$
$mg\sin \theta =f_{\max }$
$\Rightarrow mg\sin \theta =\mu N=\mu mg\cos \theta$
or $\mu =\tan \theta$
Here, $0.2=\tan \theta$ or $\cot \theta =\frac{1}{0.2}=5$
$\Rightarrow \theta ={\cot }^{-1}(5)$