Q. A cyclist is moving on a circular track of radius 80 m with a velocity$v = 36{kmh}^{- 1}$. He has to lean from the vertical approximately through an angle $(take\ g = 10{\ ms}^{- 2}$
A) $\tan^{- 1}(4)$
B) $\tan^{- 1\ }\left( \frac{1}{3} \right)$
C) $\tan^{- 1\ }\left( \frac{1}{4} \right)$
D) $\tan^{- 1\ }\left( \frac{1}{8} \right)$
Explanation
(d) Angle made by the cyclist with vertical is given by
$\tan{\theta = \frac{v^{2}}{rg}}$
$\therefore\ \theta = \tan^{- 1}\left( \frac{10 \times 10}{80 \times 10} \right)\ \left( \therefore v = 36 \times \frac{5}{18} = {10\ ms}^{- 1} \right)$
$= \tan^{- 1}\left( \frac{1}{8} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.