Question

A body takes $\frac{4}{3}$ times as much time to slide down rough inclined plane as it takes to slide down an identical but smooth inclined plane. If the angle of inclined plane is ${45}^0$, find the coefficient of friction.

• A. 7/16
• B. 9/16
• C. 7/9
• D. 3/4

Answer 1

Answer: (A)

7/16

For smooth surface, $t_s=\sqrt{\frac{2l}{gsin\theta }}$; where $l$ is distance travelled on inclined plane.

For rough surface, $t_r=\sqrt{\frac{2l}{g(sin\theta -\mu cos\theta )}}$ ; where $\mu =tan\theta$

Also, $t_r/t_s=4/3$

Solving above two equations, $\mu =\frac{7}{16}$