Question

A given object takes n times more time to slide down ${45}^{\circ }$ rough inclined plane as it takes to slide down a perfectly smooth ${45}^{\circ }$ incline. The coefficient of kinetic friction between the object and the incline is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

From $s=ut+\frac{1}{2}a{t}^2=0+\frac{1}{2}a{t}^2,t=\sqrt{\frac{2s}{a}}$

For smooth plane $a=gsin\theta$

For rough plane, $a^{\prime }=g(sin\theta -\mu cos\theta )$

$\therefore t^{\prime }=nt\Rightarrow \sqrt{\frac{2s}{g(sin\theta -\mu cos\theta )}}=n\sqrt{\frac{2s}{gsin\theta }}$

$\therefore n2g(sin\theta -\mu cos\theta )=gsin\theta$

When $gsin\theta ={45}^{\circ },sin\theta =cos\theta =\frac{1}{\sqrt{2}}$

Solving, we get $\mu =\frac{1}{1-n^2}$