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A car travels on a circular racetrack of radius 50 m, which is banked at an angle $\theta$. If the car travels at a speed 10 ms$^{-1}$, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be 10 ms$^{-2}$, the value of $\theta$ is:
Detailed Solution
Wear and tear is minimum when no friction is needed: $\tan\theta=\frac{v^2}{Rg}=\frac{(10)^2}{50\times10}=\frac{1}{5} \Rightarrow \theta=\tan^{-1}\left(\frac{1}{5}\right)$.