Q. Find the maximum speed at which a car can turn round a curve of 30 m radius on a level road if the coefficient of friction between the tyres and the road is 0.4 (Acceleration due to gravity $= {10\ ms}^{- 2})$
A) $12\ {ms\ }^{- 2}$
B) $10\ {ms\ }^{- 2}$
C) $11\ {ms\ }^{- 2}$
D) $15\ {ms\ }^{- 2}$
Explanation
(c) Centripetal force is provided by friction, so
$\frac{{mv}^{2}}{r} < f_{L}\ ie,\frac{{mv}^{2}}{r} < \mu\ mg$
$i.e,\ \ \ v < \sqrt{\mu gr}\ so\ that,\ v_{\max} = \sqrt{\mu gr}$
$Here,\ \ \ \mu = 0.4,\ r = 30m\ and\ g = 10{ms}^{- 2}$
$\therefore\ \ v_{\max} = \sqrt{0.4 \times 30 \times 10} = 11m/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.