Question

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

Answer 1

$f _{ s \max }=\frac{ mv ^{2}}{ R }$
$\mu mg =\frac{ mv { }^{2}}{ R }$
$v =\sqrt{\mu Rg }$
$\frac{ v _{2}}{ v _{1}}=\sqrt{\frac{ R _{2}}{ R _{1}}}$
$\frac{ v _{2}}{30}=\sqrt{\frac{48}{75}}$
$v _{2}=24 \,m / s$