Question

A cyclist is moving on a circular track of radius $80m$ with a velocity of $72km/hr$. He has to lean from he vertical approximately through an angle-

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

Answer 1

The correct option is C ${\tan }^{-1}\left(1/2\right)$

It is given that,

$v=72Km/hr$

$=\frac{5}{18}\times 72=20m/s$

$radiusr=80m$

Bending of a cyclist in circular motion is given by the relation as

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

$\tan \theta =\frac{20\times 20}{80\times 10}$$\theta ={\tan }^{-}\left(\frac{1}{2}\right)$