Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): A block takes twice the time to slide down a rough 45^ inclined plane as compared to a perfectly smooth 45^ inclined plane of the same length. The coefficient of kinetic friction for the rough plane is 0.75 . Reason (R): The coefficient of kinetic friction between two given surfaces is independent

Step-by-step solution

Assertion (A) is true: Let the length of the incline be L . The acceleration on the smooth incline is a_S = g 45^ . The acceleration on the rough incline is a_R = g( 45^ - _k 45^ ) . Using L = 1 2 a t^2 , we get t = 2L a . Given t_R = 2 t_S , we have: 2L a_R = 2 2L a_S a_S = 4 a_R Substituting the accelerations: g 45^ = 4 g( 45^ - _k 45^ ) Since 45^ = 45^ , this simplifies to: 1 = 4(1 - _k) 1 = 4 - 4 _k 4 _k = 3 _k = 0.75 . Reason (R) is true: The laws of friction state that the coefficient of kinetic friction is i