A boy on a cycle pedals around a circle of 20 metres radius at a...

In the circular frame the boy experiences two forces namely mg due to his own weight and centrifugal force due to his motion. Let the angle made by him with the vertical be (\theta). $$\begin{aligned} & \Rightarrow \tan \theta=\frac{\frac{\mathrm{mv}^2}{\mathrm{r}}}{\mathrm{mg}}=\frac{\mathrm{v}^2}{\mathrm{rg}} \\ & \Rightarrow \tan \theta=\frac{20^2}{20 \times 9.8} \\ & \Rightarrow \theta=63.90^{\circ} \end{aligned}$$)$