Two satellites of earth, `S_(1)` and `S_(2)` are moving in the same orbit. The mass of `S_(1)` is four times the mass of `S_(2)`. Which one of the following stetements is true ?

Options

A. The potential energies fo earth and satellite in the two cases are equal.
B. `S_(1)` and `S_(2)` are moving with the same speed.
C. The kinetic energies of the two satellites are equal.
D. The time period of `S_(1)` is four times that of `S_(2)`.

Answer

B

Explanation

The satellite of mass m is moving in a circular orbit of radius r.
`:.` Kinetic energy of a satellite, `K=(GM m)/(2r )" "`..(i)
Potential energy of a satellite, `U=(-GM m)/(r )" "`.. (ii)
Orbit speed of satellite , `v=sqrt((GM)/(r ))" "`...(iii)
Time-period of satellite, `T=[(((4pi^(2)))/(GM))r^(3)]^(1//2)" "`...(iv)
Given `m_(S_(1))=4_(m_(S_(2))`
Since M, r is same for both the satellites `S_(1)` and `S_(2)`.
`:.` From equation (ii), we get `U prop m`
`:. (U_(S_(1)))/(U_(S_(2)))=(m_(S_(1)))/(m_(S_(2)))=4" or ",K_(S_(1))=4K_(S_(2))`
Hence option (c ) is wrong.
From (iv), since T is independent of the mass of a satellite, time period is same for both the satellites `S_(1)` and `S_(2)`. Hence option (d) is is wrong.