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Question

Physics Question on laws of motion

A circular racetrack of radius 300m300 \,m is banked at an angle of 15?.15^?. The coefficient of friction between the wheels of a race car and the road is 0.20.2, the maximum permissible speed to avoid slipping is

A

18.6m18.6\, m s1s^{-1}

B

28.6m28.6\, m s1s^{-1}

C

38.6m38.6\,m s1s^{-1}

D

48.6m48.6\, m s1s^{-1}

Answer

38.6m38.6\,m s1s^{-1}

Explanation

Solution

The maximum permissible speed is given by vmaxv_{max} =Rg(μ+tanθ)1μtanθ=\sqrt{\frac{Rg\left(\mu+tan\,\theta\right)}{1-\mu \,tan\, \theta}} =300×10×(0.2+0.27)10.2×0.27=\sqrt{\frac{300\times10\times\left(0.2+0.27\right)}{1-0.2\times0.27}} =38.6m=38.6 \,m s1s^{-1}