JEE Main Physics question

PhysicsLaws of MotionJEE Main

A block moves down a smooth inclined plane of inclination θ. Its velocity on reaching the bottom is v. If it slides down a rough inclined plane of the same inclination, its velocity on reaching the bottom is v/n, where n is a number greater than 1. The coefficient of friction is given by

Answer: (A)

Solution

v² = 2gL sinθ (smooth); (v/n)² = 2gL(sinθ−μcosθ) (rough). Dividing: 1/n² = 1 − μcotθ ⟹ μ = tanθ(1−1/n²).

Question ID VK-153038