Discussion
What will be the maximum speed of a car on a circular road of radius 12 m if the coefficient of friction between the tyres and the road is 0.3? \(g = 10 ms^{-2}\)
Answer: E
The maximum speed is 6 ms-1.
On a flat circular road, friction supplies the centripetal force. The car can go no faster than the speed at which the needed force equals the maximum friction:
\[ \begin{aligned} \frac{mv^{2}}{r} &= \mu mg \\ v &= \sqrt{\mu gr} = \sqrt{0.3 \times 10 \times 12} \\ &= \sqrt{36} = 6\ \text{m s}^{-1} \end{aligned} \]
The option 36 is \(v^{2}\), forgetting the square root, and 3.6 shifts the decimal point. The mass cancels, so the answer does not depend on the car.
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