A car moves along a circular track of radius | vedclass

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(D) For a car moving on a banked circular track with friction,the maximum speed $v_{max}$ is given by the formula:$v_{max} = \sqrt{gR \left( \frac{\mu

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(D) For a car moving on a banked circular track with friction,the maximum speed $v_{max}$ is given by the formula:$v_{max} = \sqrt{gR \left( \frac{\mu + 	an 	heta}{1 - \mu 	an 	heta} ight)}$Given the banking angle $	heta = 30^o$,we know that $	an 30^o = \frac{1}{\sqrt{3}}$.Substituting this into the formula:$v_{max} = \sqrt{gR \left( \frac{\mu + \frac{1}{\sqrt{3}}}{1 - \mu \frac{1}{\sqrt{3}}} ight)}$Multiplying the numerator and denominator inside the square root by $\sqrt{3}$:$v_{max} = \sqrt{gR \left( \frac{\mu \sqrt{3} + 1}{\sqrt{3} - \mu} ight)}$Comparing this with the given options,none of the provided expressions match this result. Therefore,the correct choice is $D$.

$A$ car moves along a circular track of radius $R$ banked at an angle of $30^o$ to the horizontal. The coefficient of static friction between the wheels and the track is $\mu$. The maximum speed with which the car can move without skidding out is

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