Question

A circular curve of highway is designed for traffic moving at $72\text{km/h}$. If the radius of the curved path is $100\text{m}$, then correct angle of banking of the road should be given by
$($Take, $g=10{\text{m/s}}^2)$

• A. ${\tan }^{-1}(\frac{2}{3})$
• B. ${\tan }^{-1}(\frac{3}{5})$
• C. ${\tan }^{-1}(\frac{2}{5})$
• D. ${\tan }^{-1}(\frac{1}{4})$

Answer 1

The correct option is C ${\tan }^{-1}(\frac{2}{5})$

Given:
$R=100\text{m}$
$v=72\text{km/h}=72\times \frac{5}{18}\text{m/s}=20\text{m/s}$

Angle of banking is given by

$\theta ={\tan }^{-1}\frac{v^2}{Rg}$

$\theta ={\tan }^{-1}(\frac{{20}^2}{100\times 10})$

$\therefore \theta ={\tan }^{-1}(\frac{2}{5})$

Hence, option $\left(C\right)$ is correct.

Why this question ? Tip: This formula $v=\sqrt{Rg\tan \theta }$ is applied, when friction force is not considered.