Laws of Motion - Result Question 55

55. 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 :

[2016]

(a) $\sqrt{g R^{2}(\frac{\mu_s+\tan \theta}{1-\mu_s \tan \theta})}$

(b) $\sqrt{g R(\frac{\mu_s+\tan \theta}{1-\mu_s \tan \theta})}$

(c) $\sqrt{\frac{g}{R}(\frac{\mu_s+\tan \theta}{1-\mu_2 \tan \theta})}$

(d) $\sqrt{\frac{g}{R^{2}}(\frac{\mu_s+\tan \theta}{1-\mu_s \tan \theta})}$

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Answer:

Correct Answer: 55. (b)

Solution:

  1. (b) On a banked road,

$ \frac{V _{\max }^{2}}{Rg}=(\frac{\mu_s+\tan \theta}{1-\mu_s \tan \theta}) $

Maximum safe velocity of a car on the banked road

$ V _{\max }=\sqrt{Rg[\frac{\mu_s+\tan \theta}{1-\mu_s \tan \theta}]} $