First slide

Banking of road

Question

A circular curve of a highway is designed for traffic moving at 72 kmh^-1. If the radius of the curved path
is 100 m, the correct angle of banking of the road should be

Easy

A

$\tan^{- 1} (\frac{2}{5})$
B

$\tan^{- 1} (\frac{3}{5})$
C

$\tan^{- 1} (\frac{1}{5})$
D

$\tan^{- 1} (\frac{1}{4})$

Solution

Given, $v = 72 {kmh}^{- 1} = 72 \times \frac{5}{18} {ms}^{- 1} = 20 {ms}^{- 1}$
R = 100 m
$∴ θ = \tan^{- 1} (\frac{v^{2}}{R g}) = \tan^{- 1} (\frac{400}{100 \times 10}) = \tan^{- 1} (\frac{2}{5})$

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