Question

A cyclist on the ground goes round a circular path of circumference $34.3m$ in $\sqrt{22}sec$. The angle made by him, with the vertical, will be

• A. ${45}^{\circ }$
• B. ${40}^{\circ }$
• C. ${42}^{\circ }$
• D. ${48}^{\circ }$

Answer 1

The correct option is A ${45}^{\circ }$

Velocity of cyclist is $v=\frac{34.3}{\sqrt{22}}$ and radius of the circular path is $r=\frac{34.3}{2\pi }$
For circular motion, $\tan \theta =\frac{v^2}{rg}=\frac{{\left(\frac{34.3}{\sqrt{22}}\right)}^2}{\frac{34.3}{2\pi }\times 9.8}=1$
or $\theta ={45}^o$.