Question

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 statements is true?
A. The potential energies of 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 `S_(2)`.

Answer 1

Correct Answer - B
(b) Both orbital speed of satellite `v_(o)=sqrt((GM_(E)m)/( r))` and time period of revolution of satellite, `T=[(4pi^(2)r^(3))/(GM_(E))]^(1//2)`are independent of mass of satellite. Therefore orbital speed and time period of revolution of both the satellites are same. Hence , option (b) is correct.
The kinetic energy of a satellite, `K=-(GM_(E)m)/(r )`
and potential energy of a satellite , `U=-(GM_(E)m)/( r)`
Both depend on mass of satellite, vary with mass of satellite.