Q. A car travels on a circular racetrack of radius 50 m, which is banked at an angle θ. If the car travels at a speed 10 m s⁻¹, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be 10 m s⁻², the value of θ is:
A) $\tan^{-1}(2\sqrt3)$
B) $\tan^{-1}(1/5)$
C) $\tan^{-1}(2/5)$
D) $\tan^{-1}(\sqrt3/2)$
Explanation
[Solution from source] Tyre wear is least when no friction is needed, i.e. at the optimum banking speed: $\tan\theta=v^2/(rg)=100/(50\times10)=1/5$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.