Question

A car is moving on a circular level road of radius $300\text{m}$. If the coefficient of static friction is $0.3$, maximum safe speed (in $\text{km/h}$) of the car can be

[Take $g=10{\text{m/s}}^2$]

Answer 1

Given radius of circular level road, $r=300\text{m}$
Coefficient of static friction, $\mu =0.3$
For maximum safe speed, friction will act at its limiting value to provide necessary centripetal force and prevent skidding of car.
$f=\frac{m{v}^2}{r}$
$\Rightarrow \mu mg=\frac{m{v}^2}{r}$
$\Rightarrow v=\sqrt{\mu rg}$
$\Rightarrow v=\sqrt{0.3\times 300\times 10}$
$\therefore v=30\text{m/s}=30\times \frac{18}{5}=108\text{km/h}$
$[\because 1\text{m/s}=\frac{18}{5}\text{km/h}]$
Maximum safe speed of the car is $108\text{km/h}$.