Question

A car moves along a horizontal circular road of radius r with velocity v. The coefficient of friction between the wheels and the road is μ. Which of the following statements is not true?

(a) The car will slip if v > √(μrg).

(b) The car will slip if μ < v² / rg.

(c) The car will slip if r > v² / μg.

(d) The car will slip at a lower speed, if it moves with some tangential acceleration, than if it moves at constant speed.

Answer 1

Correct Answer is: (c) The car will slip if r > v² / μg.

The required centripetal force (mv ²/r) is supplied by the force of friction, which has a maximum value of μmg. Hence, the car will slip when mv ²/r > μmg. This yields (a) and (b) but not (c). To understand why (d) is a correct statement and, therefore, an incorrect choice,