A car of mass ' m ' moves on a banked road having radius ' r ' and banking angle θ . To avoid slipping from banked road, the maximum permissible speed of the car is v 0 . The coe

Question

A car of mass ' m ' moves on a banked road having radius ' r ' and banking angle θ . To avoid slipping from banked road, the maximum permissible speed of the car is v 0 ​ . The coefficient of friction μ between the wheels of the car and the banked road is

TestHub · Accepted Answer

So, N = m g cos θ + r m v 0 2 ​ ​ sin θ f r ​ = μ m g cos θ + r μ m v 0 2 ​ ​ sin θ ​ And r m v 0 2 ​ ​ cos θ = m g sin θ + f r ​ ⇒ r m v 0 2 ​ ​ cos θ − m g sin θ = μ ( m g cos θ + r m v 0 2 ​ ​ sin θ ) ⇒ ( v 0 2 ​ − g r tan θ ) = μ ( v 0 2 ​ tan θ + g r ) ⇒ μ = g r + v 0 2 ​ tan θ v 0 2 ​ − g r tan θ ​ ​

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