At what angle should a circular road be banked so that a car running at $50 \; km/hr$ be safe to go round the circular turn of $200 \; m$ radius?

Given,

Speed of car $(v) = 50\;km/hr = 13.89\;m/s$

Radius of circle $(r) = 200\;m$

Banking angle $(\theta) = \;?$

We know,

$tan \theta = $ $\frac{v^2}{r\;*\;g}$

$tan \theta = $ $\frac{(13.89)^2}{200\;*\;10}$ $ = 0.0964$

∴ $\theta = 5.5^{\circ}$

⇒ Banking angle $\theta = 5.5^{\circ}$

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