A car of mass m is moving on a level circular track of radiu... | Physics | SolveeIt | Solveeit

Today, August 24

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

0

C

$\sqrt{\frac{mRg}{\mu_s}}$

D

$\sqrt{\mu_s Rg}$

Answer

$\sqrt{\mu_s Rg}$

Explanation

Solution

Force of friction provides the necessary centripetal force.
$f \le \mu_s N=\frac{mv^2}{R}$
$v^2 \le \frac{\mu_s RN}{m}$
$v^2 \le \mu_s Rg\hspace25mm [\because N=mg]$
or $v \le \sqrt{\mu_s mg}$
$\therefore$ The maximum speed of the car in circular motion is
$v^{max}=\sqrt{\mu_s Rg}$