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:
- (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}]} $
