A car is negotiating a curved road of radius $$R.$$ The road is banked at an angle $$\theta .$$ the coefficient of friction between the tyres of the car and the road is $${\mu _s}.$$ The maximum safe velocity on this road is:

Solution :
On a banked road, $$\frac{{V_{\max }^2}}{{Rg}} = \left( {\frac{{{\mu _s} + \tan \theta }}{{1 - {\mu _s}\tan \theta }}} \right)$$
Maximum safe velocity of a car on the banked road
$${V_{\max }} = \sqrt {Rg\left[ {\frac{{{\mu _s} + \tan \theta }}{{1 - {\mu _s}\tan \theta }}} \right]} $$