Question

Starting from rest, the time taken by a body sliding down on a rough inclined plane at ${45}^0$ with the horizontal is twice the time taken to travel on a smooth plane of same inclination and same distance. Then the coefficient of kinetic friction is

• A. 0.25
• B. 0.33
• C. 0.5
• D. 0.75

Answer 1

The correct option is D 0.75

Time taken for the rough surface, $t_r=\sqrt{\frac{2l}{g(sin\theta -\mu cos\theta )}}$

Time taken for the smooth surface, $t_s=\sqrt{\frac{2l}{gsin\theta }};t_r=2t_s$
$\Rightarrow \sqrt{\frac{2l}{g(sin\theta -\mu cos\theta )}}=2\times \sqrt{\frac{2l}{gsin\theta }}$
$\Rightarrow 4(\sin \theta -\mu cos\theta )=\sin \theta$
$\theta ={45}^0$, $\therefore \sin \theta =\cos \theta$
$\therefore 4(1-\mu )=1$
$\mu =\frac{3}{4}$

So, $\mu =0.75$