Q117 / 160 · JIPMER 2012 · Physics
A boy on a cycle pedals around a circle of 20 metres radius at a speed of $20 \mathrm{~m} / \mathrm{s}$. The combined mass of the body and the cycle makes with the vartical so that it may not fall is $\left(g=9.8 \mathrm{~m} / \mathrm{s}^2\right)$
- A$60.25^{\circ}$
- Correct answerB$63.90^{\circ}$
- C$26.12^{\circ}$
- D$30.00^{\circ}$
Solution
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 \(\theta\).
\(\begin{aligned}
& \Rightarrow \tan \theta=\frac{\frac{\mathrm{mv}^2}{\mathrm{r}}}{\mathrm{mg}}=\frac{\mathrm{v}^2}{\mathrm{rg}} \\
& \Rightarrow \tan \theta=\frac{20^2}{20 \times 9.8} \\
& \Rightarrow \theta=63.90^{\circ}
\end{aligned}\)
Hence, the correct answer is option: 'B'.