Question

A car of mass 800 kg moves on a circular track of radius 40 m. If the coefficient of friction is 0.5, then maximum velocity with which the car can move is:

• A. 7 m/s
• B. 14 m/s
• C. 8 m/s
• D. 12 m/s

Answer 1

The correct option is B 14 m/s

When a car goes round a curved road, it requires some centripetal force. While rounding the curve, the wheels of the car have a tendency to leave the curved path and regain the straight line path. Force of friction between the wheels and the mad opposes this tendency of the wheels. This force (of friction) therefore acts, towards the centre of the circular track and provides the necessary centripetal force.
$\therefore \frac{m{v}^2}{r}\le \mu mg$
$v^2\le \mu rg$
$v\le \sqrt{\mu rg}$
Hence, the maximum velocity with which a vehicle can go round a level curve, without a skidding is $v=\sqrt{\mu rg}$
Here, $r=40m$
$\mu =0.5$
$\therefore v=\sqrt{0.5\times 40\times 9.8}$
$=14m/s$