Question

A curved in a level road has a radius $75m$. The maximum speed of a car turning this curved road can be $30m/s$ without skidding. If radius of curved road is changed to $48m$ and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ___$m/s$.

Answer 1

Answer: 24

$f_{s\max }=\frac{m{v}^2}{R}$
$\mu mg=\frac{mv{}^2}{R}$
$v=\sqrt{\mu Rg}$
$\frac{v_2}{v_1}=\sqrt{\frac{R_2}{R_1}}$
$\frac{v_2}{30}=\sqrt{\frac{48}{75}}$
$v_2=24m/s$