A smooth block is released at rest on a 45 degree incline and then slides a distance d.

Question

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

(a) µ_s = 1 - 1/n²

(b) µ_s = √(1 - 1/n²)

(c) µ_k = 1 - 1/n²

(d) µ_k = √(1 - 1/n²)

Answer 1

(c) : Component of g down the plane = gsinθ 

Therefore, For smooth plane,

d = 1/2(gsinθ )t²    ---------(i)

For rough plane,

Frictional retardation up the plane = µ_k (gcosθ)