Question

On an unbaked road, a cyclist negotiating a bend of radius $r$ at velocity $v$ must lean inwards by an angle $\theta$ equal to -

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

Answer 1

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

As we know that on an unbanked road, reaction force $R$ make some angle $\theta$ with the normal

$R\cos \theta =Mg$

$R\sin \theta =\frac{M{v}^2}{r}$

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

$\theta ={\tan }^{-1}\left(\frac{v^2}{rg}\right)$