Question

Two satellites of masses $m$ and $2m$ are revolving in a circular orbit of radius $r$ around the earth. The ratio of their frequencies of revolution will be

• A. $1:3$
• B. $1:2$
• C. $1:1$
• D. $2:1$

Hint:

Orbital motion depends on central mass, not on the mass of the orbiting body.

Answer 1

The Correct Option is C

Step 1: Expression for orbital frequency.
For a satellite in circular orbit:
\[ f = \frac{1}{2\pi}\sqrt{\frac{GM}{r^3}} \]

Step 2: Dependence on mass of satellite.
The orbital frequency depends only on the mass of the earth and radius of orbit, not on the mass of the satellite.

Step 3: Conclusion.
Both satellites have the same frequency of revolution.