First slide

Circular motion in horizontal plane

Question

A car moving with sped 10 m/s along a circular road of mean radius 50 m. The surface of the road is horizontal. What must be the minimum coefficient of friction between the road surface and tyres to avoid skidding?

Easy

A

0.3
B

0.2
C

0.5
D

0.4

Solution

$f_{\max} = μ_{m g}$
Frictional force acting on the tyres, $f = \frac{m V^{2}}{R}$
For no skidding, $f \leq f_{\max} \Rightarrow \frac{m V^{2}}{R} \leq μ m g$
$\Rightarrow μ_{\min} = \frac{V^{2}}{R g} = \frac{{(10)}^{2}}{50 \times 10} = 0.2$

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