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Q.

A curve in a level road has a radius 75m. The maximum speed of a car turning this curved road can be 30m/s without skidding. If radius of curved road is changed to 48m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ____________ m/s.

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answer is 24.

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Detailed Solution

$f_{s \max} = \frac{m v^{2}}{R} \Rightarrow μ m g = \frac{m v^{2}}{R}$

Hence, $v = \sqrt{μ R g} \Rightarrow v \propto \sqrt{R}$

$\frac{v_{2}}{v_{1}} = \sqrt{\frac{R_{2}}{R_{1}}}$

$\Rightarrow \frac{v_{2}}{30} = \sqrt{\frac{48}{75}} \Rightarrow v_{2} = 24 m / s$

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A curve in a level road has a radius 75m. The maximum speed of a car turning this curved road can be 30m/s without skidding. If radius of curved road is changed to 48m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ____________ m/s.