A given object takes n times more time to slide down a 45 o rough inclined plane as it takes to slide down a perfectly smooth 45 o incline. The coefficient of kinetic friction between the object and the incline is:

Step-by-step solution

Time taken to slide along a smooth surface is t 1 . S = 1 2 g sin ⁡ 45 o t 1 2 t 1 = 2 2 s g Time taken to slide along a rough surface is t 2 . S = 1 2 g sin ⁡ 45 o - μ g sin ⁡ 45 o   t 2 2 t 2 = 2 2 s g 1 - μ t 2 = n t 1 2 2 s g 1 - μ = n 2 × 2 2 s g ⇒ 1 - μ = 1 n 2 ⇒ μ = 1 - 1 n 2