Question

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?

• A. $v<\sqrt{{\mu }_{s}Rg}$
• B. $v\le \sqrt{{\mu }_{s}Rg}$
• C. $v<\sqrt{{\mu }_{k}Rg}$
• D. None of these

Answer 1

Answer: (B)

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,
$\frac{m{v}^2}{R}\le {\mu }_{s}mg$
$v\le \sqrt{{\mu }_{s}Rg}$
$(\because N=mg)$
Thus, when a car is moving along a circle, then its velocity $v\le \sqrt{{\mu }_{s}R}g$, so that it will not move away from the circle.