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

Question

 

$$(a)\;\mu_k=1-\frac{1}{x^2} \quad (b)\;\mu_k=\sqrt {1-\frac{1}{x^2}} \quad (c)\;\mu_s=1-\frac{1}{x^2} \quad (d)\;\mu_s=\sqrt{1-\frac{1}{x^2}}$$