First slide

Circular motion in horizontal plane

Question

The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius R and coefficient of kinetic friction μ is

Moderate

A

$μRg$
B

$Rg \sqrt{μ}$
C

$μ \sqrt{(Rg)}$
D

$\sqrt{μRg}$

Solution

Centripetal force = force of friction
$∴ \frac{{mv}^{2}}{R} = {μR}^{'} (R^{'} = reaction of ground)$
Here $R^{'} = mg$
Hence $\frac{{mv}^{2}}{R} = μmg v = \sqrt{(μRg)}$

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