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 types of the car and the road is $\mu_s$. The maximum safe velocity on this road is :

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

Answer 1

Answer: (A)

$\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]} $