Question

A body takes time ‘t’ to reach the bottom of an inclined plane of angle $\theta$ with the horizontal. If the plane is made rough, time taken now is 2t. The coefficient of friction of the rough surface is:

• A. $\frac{3tan\theta }{4}$
• B. $\frac{2tan\theta }{3}$
• C. $\frac{tan\theta }{4}$
• D. $\frac{tan\theta }{2}$

Answer 1

The correct option is A

$\frac{3tan\theta }{4}$

$a=gsin\theta S_1=\frac{1}{2}g[sin\theta -ucos\theta ](2t{)}^2{S}_1=S_2\frac{1}{2}gsin\theta t^2=\frac{1}{2}g[sin\theta -\mu cos\theta ]4t^{2}sin\theta =4sin\theta -4\mu cos\theta 4\mu cos\theta =3sin\theta \mu =\frac{3}{4}tan\theta$