First slide

Circular motion in horizontal plane

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 $\large \mu$ . Which of the following statement is not true?

Moderate

A

The car will slip if $\large v > \sqrt {\mu rg}$
B

The car will slip if $\large \mu < \frac{{{v^2}}}{{rg}}$
C

The car will slip if $\large \mu > \frac{{{v^2}}}{{\mu g}}$
D

the car will slip at lower speed, if it moves with some tangential acceleration, than if it moves at constant speed.

Solution

Centripetal force is supplied by the frictional force of where f = mV² / r.
Now , f_max = µ . mg
.: The car will slip if f > f_max
i,e if mV² / r > µ mg
i.e if r < V²/µg

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