Laws Of Motion Question 348
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:
Options:
A) $ \sqrt{gR^{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 }} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] On a banked road, $ \frac{v^{2}\max }{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 } ]} $
