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(D) For a car moving on a circular unbanked road,the necessary centripetal force is provided by the static frictional force between the tires and the

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$\sqrt{\mu Rg}$

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(D) For a car moving on a circular unbanked road,the necessary centripetal force is provided by the static frictional force between the tires and the road surface.Let $m$ be the mass of the car,$v$ be its speed,and $R$ be the radius of the circular path.The centripetal force required is $F_c = \frac{mv^2}{R}$.The maximum static frictional force available is $f_{max} = \mu N = \mu mg$,where $N = mg$ is the normal force.To avoid skidding,the centripetal force must be less than or equal to the maximum static friction:$\frac{mv^2}{R} \leq \mu mg$$v^2 \leq \mu Rg$$v_{max} = \sqrt{\mu Rg}$.

The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius $R$ and coefficient of static friction $\mu$ is

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