A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the tyres of the car and the road is μs. The maximum safe velocity on this road is

For vertical equilibrium on the road, Ncosθ=mg+fsinθmg=Ncosθ-fsinθ……….(1)Centripetal force for safe turning, Nsinθ+fcosθ=mv2R…….(2)From eqns. (i) and (ii), we get v2Rg=Nsinθ+fcosθNcosθ-fsinθ⇒vmax2Rg=Nsinθ+μsNcosθNcosθ-μsNsinθvmax=Rgμs+tanθ1-μstanθ