Question

A body takes time t to reach the bottom of an inclined plane of angle theta with the horizontal. If the planes made rough, time taken now is 2t. The coefficient of friction of the rough surface is​

Answer 1

Answer:

$2 \tan( \theta)$

Explanation:

We know

$s = ut + \frac{1}{2} a {t}^{2}$

When there is no friction acceleration is gsin0

and when there is u friction surface acceleration will be gsin0 - ugcos0

( See your other questions i answered how )

s is same in both condition . u = 0

$\frac{1}{2} (g \sin( \theta) ) {}^{2} = \frac{1}{2} (g \sin( \theta) - \mu \: g \cos( \theta) ) {}^{2} \\ (\sin( \theta) ) {}^{2} = ( \sin( \theta) ) {}^{2} + ( \mu \: \cos( \theta) ){}^{2} - 2 \mu \sin( \theta) \cos( \theta) \\ { \mu}^{2} \cos {}^{2} ( \theta) = 2 \mu \sin( \theta) \cos( \theta) \\ \mu = 2 \tan( \theta)$