Question

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

• A. $\sqrt{Rg/{\mu }_s}$
• B. $\sqrt{mRg/{\mu }_s}$
• C. $\sqrt{{\mu }_{s}Rg}$
• D. $\sqrt{{\mu }_{s}mRg}$

Answer 1

Answer: (C)

$\sqrt{{\mu }_{s}Rg}$

For the car to stay in contact with the track, the frictional force is equal to the centripetal force.
${\mu }_{s}mg\ge \frac{m{v}^2}{R}$
$v\le \sqrt{{\mu }_{s}Rg}$
$\therefore$ $v_{max}=\sqrt{{\mu }_{s}Rg}$