Question

A circular track of radius $100$ m is designed for an average speed $54$ km/h. Find the angle of banking.

• A. ${\tan }^{-1}\left(\frac{3}{20}\right)$
• B. ${\tan }^{-1}\left(\frac{9}{40}\right)$
• C. ${\tan }^{-1}\left(\frac{3}{10}\right)$
• D. None of these

Answer 1

Answer: (B)

${\tan }^{-1}\left(\frac{9}{40}\right)$

$\tan \theta =\frac{v^2}{rg}$

$=\frac{15\times 15}{100\times 10}=\frac{9}{40}$

$\theta ={\tan }^{-1}\left(\frac{9}{40}\right)$