1. Tardigrade
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  3. Physics
  4. An unbanked circular highway curve on the level ground makes a turn of 90° . The highway carries traffic at 108 km h- 1 , and the centripetal force on a vehicle is not to exceed (1/1 0) of its weight. What is the approximate minimum length of the curve, in km?

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Q. An unbanked circular highway curve on the level ground makes a turn of $90^\circ $ . The highway carries traffic at $108 \, km \, h^{- 1}$ , and the centripetal force on a vehicle is not to exceed $\frac{1}{1 0}$ of its weight. What is the approximate minimum length of the curve, in km?

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

$\frac{m v^{2}}{R}=\frac{m g}{1 0}$
$R=\frac{1 0 v^{2}}{g}=\left(\text{108} \times \frac{5}{1 8}\right)^{2}=900\text{m}$ ,
Length $\frac{\pi R}{2}=\text{1.413 km}$