Question

A car is negotiating a curve of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between tyres and road is $\mu$. The maximum safe velocity is

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

Answer 1

The correct option is A $\sqrt{gR\left[\frac{\mu +\tan \theta }{1-\mu \tan \theta }\right]}$

Answer (1)
$V_{\text{max}}={\left[Rg\frac{{\mu }_{\text{s}}+\tan \theta }{1-{\mu }_{\text{s}}\tan \theta }\right]}^{1/2}$