MHT CET · Physics · Gravitation
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 time period of \(S_{1}\) is four times that of \(S_{2}\)
- B The potential energies of earth and satellite in the two cases are equal
- C \(S_{1}\) and \(S_{2}\) are moving with the same speed
- D The kinetic energies of the two satellites are equal
Answer & Solution
Correct Answer
(C) \(S_{1}\) and \(S_{2}\) are moving with the same speed
Step-by-step Solution
Detailed explanation
When two satellites of earth are moving in same orbit, then time period of both are equal. From Kepler's third law
\(T^{2} \propto r^{3}\)
Time period is independent of mass, hence their time periods will be equal. The potential energy and kinetic energy are mass dependent, hence the PE and \(\mathrm{KE}\) of satellites are not equal. But, if they are orbiting in a same orbit, then they have equal orbital speed.
\(T^{2} \propto r^{3}\)
Time period is independent of mass, hence their time periods will be equal. The potential energy and kinetic energy are mass dependent, hence the PE and \(\mathrm{KE}\) of satellites are not equal. But, if they are orbiting in a same orbit, then they have equal orbital speed.
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