First slide

Motion of planets and satellites

Question

Two satellites A and B of the same mass are revolving around the earth in the concentric circular orbits such that the distance of satellite B from the centre of the earth is thrice as compared to the distance of the satellite A from the centre of the earth. The ratio of the centripetal force acting on B as compared to that on A is

Moderate

A

$\frac{1}{3}$
B

$3$
C

$\frac{1}{9}$
D

$\frac{1}{\sqrt{3}}$

Solution

$V_{A} = \sqrt{\frac{GM}{r_{A}}} and V_{B} = \sqrt{\frac{GM}{r_{B}}}$
$Given r_{B} = 3 r_{A}$
$Now F_{A} = \frac{{mv}_{A}^{2}}{r_{A}} = \frac{M}{r_{A}} \frac{GM}{r_{A}} = \frac{GMm}{r_{A}^{2}}$
$\begin{aligned} F_{B} = \frac{GMm}{r_{B}^{2}} \\ \frac{F_{B}}{F_{A}} = \frac{r_{A}^{2}}{r_{B}^{2}} = \frac{1}{9} \end{aligned}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App