Laws of Motion

JEE Main level, numerical answer, medium

205 of 210

Question 205 of 210

A curved in a level road has a radius 75m75m. The maximum speed of a car turning this curved road can be 30ms−130m{s}^{-1} without skidding. If radius of curved road is changed to 48m48m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be _____ ms−1m{s}^{-1}.

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Answer: 24

The maximum speed is given as v=μgrv=\sqrt{\mu gr}, where, μ\mu is coefficient of friction and rr is radius of curved road.
⇒v1v2=r1r2\Rightarrow \dfrac{{v}_{1}}{{v}_{2}}=\sqrt{\dfrac{{r}_{1}}{{r}_{2}}}
⇒30v2=7548=2516=54\Rightarrow \dfrac{30}{{v}_{2}}=\sqrt{\dfrac{75}{48}}=\sqrt{\dfrac{25}{16}}=\dfrac{5}{4}
⇒v2=24ms−1\Rightarrow {v}_{2}=24m{s}^{-1}

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