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Two satellites of earth S(1) and S(2) ar...

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)`.

Text Solution

Verified by Experts

The correct Answer is:
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.
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