Q 11-04-003NEETNEET 2026Top questionEasy
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 $10\ \text{m s}^{-1}$, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be $10\ \text{m s}^{-2}$, the value of $\theta$ is :
Answer: (A) $\tan^{-1}\left(\dfrac{1}{5}\right)$
Wear and tear is minimum when no friction is needed, i.e. at the optimum banking speed:
$$\tan\theta = \frac{v^2}{rg} = \frac{10^2}{50 \times 10} = \frac{1}{5}$$
$$\theta = \tan^{-1}\left(\frac{1}{5}\right)$$
Solution by Sreeraj P, M.Sc Physics