A smooth block is released at rest on a $45^{\circ}$ incline and then slides a distance $d$. The time taken to slide is $n$ times as much to slide on rough inclined than on a smooth incline. The coefficient of friction is :

Question

( A ) $\mu_s = \sqrt{1 - \frac{1}{n^2}}$
( B ) $\mu_s = \sqrt{1 - \frac{1}{n^2}}$
( C ) $\mu_k = \sqrt{1 - \frac{1}{n^2}}$
( D ) $\mu_k = 1 - \frac{1}{n^2}$