A block of mass m is placed on a vertical fixed circular track and then it is given velocity v along the track at position A on track. The coefficient of friction between the block and the track varies with the angle θ . If the block moves on track with constant speed then the coefficient of friction is

Step-by-step solution

Since the block is moving with a constant speed, at any instant its tangential acceleration is zero. Hence, f = m g s i n θ Also, N - m g c o s θ = m v 2 R N = m v 2 R + m g cos θ f = μ N = μ m v 2 R + μ m g cos θ m g sin θ = μ m v 2 R + μ m g cos θ ⇒ μ = s i n θ c o s θ + v 2 R   g