The time taken by an object to slide down 45 ° rough inclined plane is n times as it takes to slide down a perfectly smooth 45 ° incline plane. The coefficient of kinetic friction between the object and the incline plane is:

Step-by-step solution

Let angle of inclination is θ = 45 ° . Then, acceleration along the incline in case of smooth incline will be, a 1 = g   sin θ = g 2 . In case of rough incline, kinetic friction will act against the direction of motion. Normal force acting on the object will be m g cos θ . Therefore, acceleration along the incline in case of rough incline will be, a 2 = g   sin θ - μ g   cos θ = g 2 - μ g 2 . Now as per question, t 2 = n t 1 and as the displacement covered is t