Question

A frictionless track has a curve of radius $90\sqrt{3}\text{m}$. If the speed limit on this road is $30\text{m/s}$, what should be the banking angle for this road to ensure safe driving ? Take $g=10{\text{m/s}}^2$.

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is A ${60}^{\circ }$

From the condition of banking for a frictionless circular road: $\tan \theta =\frac{v^2}{rg}$
For $v=v_{max}=30\text{m/s}$,
$\tan \theta =\frac{{30}^2}{\frac{90}{\sqrt{3}}\times 10}=\sqrt{3}$
$\Rightarrow \theta ={\tan }^{-1}\left(\sqrt{3}\right)={60}^{\circ }$
Hence the road should be banked at an angle of ${60}^{\circ }.$