Discussion
Ranjan is moving with his race car on a circular racetrack of radius 200 m and it is banked at an angle of 10°. If the coefficient of friction between the wheels of the race car and the road is 0.2, then find the optimum speed of the race car to avoid wear and tear on its tyres.
Answer: B
The speed at which a car needs no friction at all on a banked curve is \(v = \sqrt{rg\tan\theta}\). At this speed the tyres do not rub sideways against the road, which is the optimum speed to avoid wear and tear. With r = 200 m, g = 10 m/s\(^2\) and \(\tan 10^\circ = 0.1763\):
\[ \begin{aligned} v = \sqrt{200 \times 10 \times 0.1763} \\ &= \sqrt{352.7} = 18.78\ \text{m/s} \end{aligned} \]The given coefficient of friction 0.2 is not used, because it only determines the maximum safe speed (about 27 m/s), not the optimum one. The other options do not follow from either speed.
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