A circular racetrack of radius $300 m$ is banked at an angle of $15 °$ . If the coefficient of friction between the wheels of a racing car and the road is $0.2$ , the maximum permissible speed (in $m s^{- 1}$ ) to avoid slipping is
(Take $\tan 15 ° = 0.27$ )

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$39.2 m s^{- 1}$

$38.2 m s^{- 1}$

$38.5 m s^{- 1}$

$38 m s^{- 1}$

answer is B.

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Detailed Solution

Here $R = 300 m, θ = 15 °, g = 9.8 m s^{- 2}, μ = 0.2$

The maximum permissible speed is given by

$v_{m a x} = \sqrt{\frac{R g (μ + \tan θ)}{1 - μ \tan θ}} = \sqrt{\frac{300 \times 9.8 \times (0.2 + 0.27)}{1 - 0.2 \times 0.27}} = 38.2 m s^{- 1}$

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