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A car of mass m is moving on a level circular track of radius R. If $\mu_s$ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by
A
$\sqrt{\mu_sRg}$
B
$\sqrt{\mu_smRg}$
C
$\sqrt{Rg/\mu_s}$
D
$\sqrt{mRg/\mu_s}$
Detailed Solution
On a level road the centripetal force is provided by static friction: $\frac{mv^2}{R} \le \mu_sN = \mu_smg$
$v^2 \le \mu_sRg$
$v_{max} = \sqrt{\mu_sRg}$
$v^2 \le \mu_sRg$
$v_{max} = \sqrt{\mu_sRg}$