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
AIPMT 2012, Medium
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Force of friction provides the necessary centripetal force.
$f \leq \mu_{s} N=\frac{m w^{2}}{R}$
$v^{2} \leq \frac{\mu_{s} R N}{m}$
$v^{2} \leq \mu_{s} R g \quad[\because N=m g]$
$v \leq \sqrt{\mu_{s} m g}$
The maximum speed of the car in circular motion is $v_{\max }=\sqrt{\mu_{s} R g}$
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