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 $\omega /8$ then the radius of the orbit will be

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

Answer 1

The correct option is A $4r$

The time period of revolution of a satellite and radius of circular orbit is related as

$T^2\propto R^3$

And, using $\omega =\frac{2\pi }{T}$, we get

${\omega }^2\propto \frac{1}{R^3}$

$\Rightarrow (\frac{{\omega }_1}{{\omega }_2}{)}^2=(\frac{R_2}{R_1}{)}^3$

Here, ${\omega }_1=\omega ;{\omega }_2=\omega /8;R_1=r$

$R_2=(\frac{\omega }{\omega /8}{)}^{2/3}r=4r$

Hence, option $\left(a\right)$ is correct.

Key Concept: The time period of revolution of a satellite and radius of circular orbit is related as $T^2\propto R^3$