Question

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

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

Answer 1

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

The correct angle of banking is given by,
$\tan \theta =\frac{v^2}{rg}$
Given, $v=72\text{km/h}=72\times \frac{5}{18}=20\text{m/s}$
$r=100\text{m},g=10{\text{m/s}}^2$
$\tan \theta =\frac{v^2}{rg}=\frac{{20}^2}{100\times 10}=\frac{2}{5}$
$\Rightarrow \theta ={\tan }^{-1}\left(\frac{2}{5}\right)$