Question

A block placed on an inclined plane of slope angle $\theta$ slides down with a constant speed. The coefficient of kinetic friction is equal to
(correct answer + 1, wrong answer - 0.25)

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

Answer 1

The correct option is C $\tan \theta$

Let the mass of the block in $m$ be placed on an inclined plane of slope angle $\theta$.
Block slides down with a constant speed.
Free body diagram:
Applying equilibrium in vertical direction of block,
(Normal force) $N=mg\cos \theta$ ... (1)
As frictional force is $f=\mu N$ ... (2)
From equation (1) and (2),
$f=\mu mg\cos \theta$
Applying equilibrium in horizontal direction for block,
$mg\sin \theta =\mu mg\cos \theta$
$\mu =\tan \theta$