Question

A satellite of mass $m$ revolves round the Earth of mass $M$, in a circular orbit of radius $r$, with an angular velocity $\omega$. If the angular velocity is $\frac{\omega }{8}$, the radius of the orbit will be

• A. $4r$
• B. $2r$
• C. $8r$
• D. $r$

Answer 1

The correct option is A $4r$

$T^2\propto r^3$ , where $T$ is the Time period of revolution and $r$ is the radius of the planet .
$T=\frac{2\pi }{\omega }$
$\therefore$ ${\omega }^2\propto \frac{1}{r^3}$
$\Rightarrow \frac{\frac{{\omega }^2}{8^2}}{{\omega }^2}=\frac{r^3}{{r_1}^3}$
$\Rightarrow \frac{1}{8^2}=\frac{r^3}{{r_1}^3}$
$\Rightarrow r_1^3=64r^3$

Hence , $r_1=4r$