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

Answer 1

The correct option is B $\sqrt{{\mu }_{s}Rg}$


As the car is moving in the circular path, so the forces acting on the car is shown in the above figure.

Condition for maximum speed of car in circular motion is given by,

$f=f_s\ge \frac{m{v}^2}{R}$

$\Rightarrow {\mu }_{s}N\ge \frac{m{v}^2}{R}$

$\Rightarrow {\mu }_{s}mg\ge \frac{m{v}^2}{R}$

$\Rightarrow v^2\le {\mu }_{s}Rg$

$\Rightarrow v_{max}^2={\mu }_{s}Rg$

$\therefore v_{max}=\sqrt{{\mu }_{s}Rg}$

Hence, $\left(A\right)$ is the correct answer.