question_answer

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?         [AIPMT (S) 2007]

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

Correct Answer: C

Solution :

Key Idea: In same orbit, orbital speed of satellites remains same.

When two satellites of earth are moving in same orbit, then time period of both ate equal.

From Kepler's third law

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 KE of satellites are not equal.

But, if they are orbiting in a same orbit, then they have equal orbital speed.