Question

A car moves at a speed of $20m{s}^{-1}$ on a banked track and describes an arc of a circle of radius $40\sqrt{3}$. The angle of banking is (take, $g=10m{s}^{-2})$.

• A. ${25}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${30}^{\circ }$
• E. ${40}^{\circ }$

Answer 1

The correct option is D ${30}^{\circ }$

Given, $v=20m{s}^{-1}$
$r=40\sqrt{2}m$
$\Rightarrow g=10m{s}^{-2}$
We know that, $\tan \theta =\frac{v^2}{rg}$
$\Rightarrow \tan \theta =\frac{(20{)}^2}{40\sqrt{3}\times 10}$
$\Rightarrow \tan \theta =\frac{1}{\sqrt{3}}$ or $\theta ={\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
$\Rightarrow \theta ={30}^{\circ }$.