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Physics · LAWS OF MOTION
हिन्दीA car moves along a banked circular road of radius \( R \) inclined at an angle \( \theta \) with the horizontal. If the coefficient of static friction between the tyres and the road is \( \mu_s \) (where \( \mu_s < \tan\theta \)), which of the following expressions gives the minimum speed \( v_{\min} \) required to prevent the car from sliding down the slope?
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Correct answer · Option A
\( \sqrt{R g \frac{\tan\theta - \mu_s}{1 + \mu_s \tan\theta}} \)
Explanation
For minimum speed, friction \( f = \mu_s N \) acts up the incline. Vertical balance gives \( N(\cos\theta + \mu_s \sin\theta) = mg \) and centripetal force gives \( N(\sin\theta - \mu_s \cos\theta) = \frac{m v_{\min}^2}{R} \). Dividing the two equations yields \( v_{\min} = \sqrt{R g \frac{\tan\theta - \mu_s}{1 + \mu_s \tan\theta}} \).
