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Q.
If a car is moving in uniform circular motion, then what should be the value of velocity of a car, so that car will not move away from the circle?
Laws of Motion
Solution:
For car of mass $M$ moving in circle of radius $R$, with velocity $v$, requires a centripetal force which is obtained from friction force $\left(\mu_{s} N\right)$ between the tyre of car and road, that satisfies the following condition,
$\frac{m v^{2}}{R} \leq \mu_{s} m g$
$v \leq \sqrt{\mu_{s} R g}$
$(\because N=m g)$
Thus, when a car is moving along a circle, then its velocity $v \leq \sqrt{\mu_{s} R} g$, so that it will not move away from the circle.