Two satellites of earth, S1 and S2 are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true? (a) The potential energies of earth and satellite in the two cases are equal. (b) S1 and S2 are moving with the same speed. (c) The kinetic energies of the two satellites are equal. (d) The time period of S1 is four times that of S2.

Answer: (b). Orbital speed v = √(GM/r) does not depend on the satellite's mass. Same orbit, so same speed and same period T = (2π r)/(v). PE = -GMm/r and KE = GMm/2r depend on m, so they differ (S1 has 4 times S2's). So the answer is (b) S1 and S2 move with the same speed.

Two satellites of earth, S1 and S2 are moving in the same orbit. The… | NEET 2007 (AIPMT)

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Satellites - Orbital Velocity & Period

Two satellites of earth, S1 and S2 are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?

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Answer: (b)

Orbital speed $v = \sqrt{\frac{GM}{r}}$ does not depend on the satellite's mass.
Same orbit, so same speed and same period $T = \frac{2\pi r}{v}$ .
PE $= -\frac{GMm}{r}$ and KE $= \frac{GMm}{2r}$ depend on $m$ , so they differ (S1 has 4 times S2's).
So the answer is (b) S1 and S2 move with the same speed.

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