First slide

Banking of road

Question

For traffic moving at 60 km/ hour along a circular track of radius 0⋅1 km, the correct angle of banking is

Moderate

A

$\{(60)^{2} / 0 \cdot 1)\} km$
B

$\tan^{- 1} [\frac{(50 / 3)^{2}}{100 \times 9 \cdot 8}]$
C

$\tan^{- 1} [\frac{100 \times 9 \cdot 8}{(50 / 3)^{2}}]$
D

$\tan^{- 1} \sqrt{(60 \times 0 \cdot 1 \times 9 \cdot 8)}$

Solution

$θ = \tan^{- 1} (\frac{v^{2}}{rg})$
Here $v = \frac{60 \times 10^{3}}{60 \times 60} = (50 / 3)$
$r = 0 \cdot 1 km = 100 m and g = 9 \cdot 8 m / \sec^{2}$
$∴ θ = \tan^{- 1} \{\frac{(50 / 3)^{2}}{100 \times 9 .8}\}$

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