An object is placed on the surface of a smooth inclined plane of inclination $\theta$. It takes time t, to reach the bottom. If the same object is allowed to slide down a rough inclined plane of inclination q, it takes time n t to reach the bottom where n is a number greater than one. The coefficient of friction $\mu$ is given by

• A

  $\mathrm{\mu }=\tan \mathrm{\theta }\left(1-\frac{1}{{\mathrm{n}}^2}\right)$

• B

  $\mathrm{\mu }=\cot \mathrm{\theta }\left(1-\frac{1}{{\mathrm{n}}^2}\right)$

• C

  $\mathrm{\mu }=\tan \mathrm{\theta }{\left(1-\frac{1}{{\mathrm{n}}^2}\right)}^{1/2}$

• D

  $\mathrm{\mu }=\cot \mathrm{\theta }{\left(1-\frac{1}{{\mathrm{n}}^2}\right)}^{1/2}$