Q135 / 180 · JIPMER 2019 · Physics
A particle of mass 7 kg is executing circular motion with time period of 11 sec . Find out centripetal force, if radius of circle is 10 m .
- A$\frac{30}{7} \mathrm{~N}$
- B$\frac{40}{7} \mathrm{~N}$
- C30 N
- Correct answerD$\frac{160}{7} \mathrm{~N}$
Solution
Given, Time period $(\mathrm{T})=11 \mathrm{sec}$, mass of particle $(\mathrm{m})=7 \mathrm{~kg}$
and $\quad$ radius $(\mathrm{r})=10 \mathrm{~m}$
$\therefore \quad$ Speed of particle, $v=\frac{2 \pi r}{T}=\frac{2 \times \frac{22}{7} \times 10}{11}$ $=\frac{40}{7} \mathrm{~m} / \mathrm{s}$
$\therefore$ Centripetal force, $\mathrm{F}=\frac{\mathrm{mv}^2}{\mathrm{r}}=\frac{7 \times \frac{40}{7} \times \frac{40}{7}}{10}=\frac{160}{7} \mathrm{~N}$
Hence, the correct answer is option: 'D'.