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) $\tan^{-1}\left(\dfrac{1}{5}\right)$
Concept. Wear is least when no friction is needed: $\tan\theta = \dfrac{v^2}{rg}$.
Step 1. Substitute. $\tan\theta = \dfrac{100}{500} = \dfrac15$.
Answer. $\tan^{-1}\left(\dfrac15\right)$ (Option A).
Solution by Sreeraj P, M.Sc Physics