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A circular racetrack of radius 300 m is banked at an angle of 15^o. The coefficient of friction between the wheels of a race car and the road is 0.2. The optimum speed of the race car to avoid wear and tear on its tyres is (Take $\tan 15 ° = 0.27, g = 10 m s^{- 2}$ ).

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$10 \sqrt{3} m s^{- 1}$

$9 \sqrt{10} m s^{- 1}$

$\sqrt{10} m s^{- 1}$

$2 \sqrt{10} m s^{- 1}$

answer is B.

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Detailed Solution

Here, $R = 300 m, θ = 15 °, g = 10 m s^{- 2}, μ = 0.2$

The optimum speed of the car to avoid wear and tear is given by

$v = \sqrt{R g \tan θ} = \sqrt{300 \times 10 \times \tan 15 °} = \sqrt{810} = 9 \sqrt{10} m s^{- 1}$

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