Question

A turn has a radius of $10m$. If a vehicle goes round it at an average speed of $18$ km/h, what should be the proper angle of banking?

• A. ${\tan }^{-1}\left(1/4\right)$
• B. ${\tan }^{-1}\left(1/2\right)$
• C. ${\tan }^{-1}\left(3/4\right)$
• D. ${\tan }^{-1}\left(5/7\right)$

Answer 1

The correct option is A ${\tan }^{-1}\left(1/4\right)$

Given : $r=10$ m

Average speed of the vehicle $v=18km/hr=18\times \frac{5}{18}=5$ $m/s$

Let the proper banking angle be $\theta$

Using $tan\theta =\frac{v^2}{gr}$

$\therefore$ $tan\theta =\frac{5^2}{10\times 10}$ $⟹\theta =ta{n}^{-1}\left(1/4\right)$