Two satellite of mass `m` and `9 m` are orbiting a planet in orbits of radius `R`. Their periods of revolution will be in the ratio of

Options

A. `1:9`
B. `1:3`
C. `1:1`
D. `3:1`

Answer

C

Explanation

Time period of revolution of satellite,
` T = (2pi r)/(v) = (2pi r)/(R sqrt(g//r))`
Frequency of revolution, ` v = 1/T = (Rg^(1//2))/(2pir^(3//2))`
As `v` is independent of mass of the satellite, so the frequency of revolution of both the satellites for a given circular orbit is the same.