Question

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

• A. $\sqrt{g{R}^2\frac{{\mu }_s+\tan \theta }{1-{\mu }_s\tan \theta }}$
• B. $\sqrt{gR\frac{{\mu }_s+\tan \theta }{1-{\mu }_s\tan \theta }}$
• C. $\sqrt{\frac{g}{R}\frac{{\mu }_s+\tan \theta }{1-{\mu }_s\tan \theta }}$
• D. $\sqrt{\frac{g}{R^2}\frac{{\mu }_s+\tan \theta }{1-{\mu }_s\tan \theta }}$

Answer 1

The correct option is B $\sqrt{gR\frac{{\mu }_s+\tan \theta }{1-{\mu }_s\tan \theta }}$

Given: Radius of the curved road $=R$

Coefficient of friction $=\mu$

$\Rightarrow \frac{v^2}{Rg}=\left(\frac{{\mu }_s+tan\theta }{1-{\mu }_{s}tan\theta }\right)$

$\Rightarrow v=\sqrt{Rg\left(\frac{{\mu }_s+tan\theta }{1-{\mu }_{s}tan\theta }\right)}$