First slide

Circular motion in horizontal plane

Question

A car of mass m is moving on a level circular track of radius R. If $μ_{s}$ represents the coefficient of static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by:

Moderate

A

$\sqrt{mRg / μ_{s}}$
B

$\sqrt{μ_{s} R g}$
C

$\sqrt{μ_{s} m R g}$
D

$\sqrt{R g / μ_{s}}$

Solution

$∵ f_{ms} ⩾ \frac{{mv}^{2}}{R}$
$∴ μ_{s} m g ⩾ \frac{{mv}^{2}}{R}$
$∴ \sqrt{μ_{s} R T} ⩾ V$
$∴ V_{\max} = \sqrt{μ_{s} R g}$

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