Physics - NLM Question with Solution | TestHub

The centripetal acceleration of a body moving in a circular orbit of radius $r$ with angular velocity $\omega$ is given by $a=r{\omega }^2$.

Since the time periods of both bodies are the same ($T_1=T_2=T$), their angular velocities are also the same, as $\omega =\frac{2\pi }{T}$.

For the first body of mass $10$ kg in an orbit of radius $R$, the centripetal acceleration is $a_1=R{\omega }^2$.

For the second body of mass $5$ kg in an orbit of radius $r$, the centripetal acceleration is $a_2=r{\omega }^2$.

The ratio of their centripetal accelerations is:

$\frac{a_1}{a_2}=\frac{R{\omega }^2}{r{\omega }^2}=\frac{R}{r}$

Answer: $\mathrm{R}/\mathrm{r}$