A car of mass $m$ is moving on a level circular track of radius $R$. If $\mu_s$ represents the static…
A car of mass $m$ is moving on a level circular track of radius $R$. If $\mu_s$ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by
$\sqrt{\mu_s m R g}$
$\sqrt{R g / \mu_s}$
$\sqrt{m R g / \mu_s}$
$\sqrt{\mu_s R g}$
Solution
In this condition, centripetal force is equal to static frictional force between road and tyres, so
$\begin{aligned}
\mu_s m g & =\frac{m v^2}{R} \\
v_{\max } & =\sqrt{\mu_s R g}
\end{aligned}$