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 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 1

Answer: (C)

$S_1$ and $S_2$ are moving with the same speed

Answer 2

$K.E. =\frac{ GMm }{2r}$ $\Rightarrow$ Kinetic energies are unequal.
$T =\frac{2 \pi r ^{\frac 32}}{\sqrt{ GM }}$ $\Rightarrow$ Time period are equal.
P.E. $=-\frac{\text {GMm}}{r}$ $\Rightarrow$ Potential energies are unequal.
$v =\sqrt{\frac{ GM }{ r }}$ $\Rightarrow$ Orbital speeds are equal.

So, the cortrect option is (C): $S_1$​ and $S_2$​ are moving with the same speed.