Question

There is a circular track of radius $400m$. For traffic moving at $72km/h$. What is the correct angle of banking of the road?

• A. ${30}^{\circ }$
• B. ${37}^{\circ }$
• C. ${45}^{\circ }$
• D. ${5.7}^{\circ }$

Answer 1

The correct option is D ${5.7}^{\circ }$

Converting speed to suitable units: $72km/h=20m/s$

Angle of banking is given by $\theta ={\tan }^{-1}\left(\frac{v^2}{rg}\right)$

$\Rightarrow \theta ={\tan }^{-1}\left(\frac{{20}^2}{400\times 10}\right)$

$\therefore \theta ={\tan }^{-1}\left(\frac{1}{10}\right)\approx {5.7}^{\circ }$

$\to QED.$