Question

When a car of mass \( m \) is moving with speed \( v \) along a circle of radius \( r \) on a level road, the centripetal force is provided by \( f \), where \( f \) denotes

• A. \( \frac{mv^2}{r} = f \leq \mu_s N \)
• B. \( f < \mu_k = \frac{mv^2}{r} \)
• C. \( f = \mu_s N = \frac{mv^2}{r} \)
• D. \( f = \mu_k N = \frac{mv^2}{r} \)

Hint:

Centripetal force in circular motion on flat road is always provided by static friction, not kinetic.

Answer 1

The Correct Option is A

The required centripetal force to keep a car moving in a circular path is: \[ f = \frac{mv^2}{r} \] This force is provided by static friction on a level road, not kinetic. The maximum value of static friction is \( f_{\text{max}} = \mu_s N \). So for the car to maintain circular motion safely, \[ f \leq \mu_s N \] Thus: \[ \frac{mv^2}{r} \leq \mu_s N \]