Question

A body takes time $t$ to reach the bottom of an inclined plane of angle $\theta$ will the horizontal. if the plane made rough, time takes now is $2t$. The coefficient of frcition of the rough surface is

• A. $\frac{3}{4}\tan \theta$
• B. $\frac{1}{2}\tan \theta$
• C. $\frac{2}{5}\tan \theta$
• D. $\frac{1}{4}\tan \theta$

Answer 1

The correct option is A $\frac{3}{4}\tan \theta$

we have,

length of incline,

$s=\frac{1}{2}g\sin \theta t^2$......(1)

friction force,

$f=\mu N=\mu mg\cos \theta$

$a=(\sin \theta -\mu \cos \theta )g$

$\therefore s=\frac{1}{2}\times (\sin \theta -\mu \cos \theta )g\times (2t{)}^2$.........(2)

from (1) and (2), we have,

$\sin \theta =(\sin \theta -\mu \cos \theta )4$

$\therefore \mu =\frac{3}{4}\tan \theta$