Two satellites of earth, $\mathrm{S}_1$ and $\mathrm{S}_2$ are moving in the same orbit. The mass of $S_1$…

Two satellites of earth, $\mathrm{S}_1$ and $\mathrm{S}_2$ are moving in the same orbit. The mass of $S_1$ of four times the mass of $S_2$. Which one of the following statements is true?
  1. The potential energies of earth and satellite in the two cases are equal.
  2. $S_1$ and $S_2$ are moving with the same speed
  3. The kinetic energies of the two satellites are equal
  4. The time period of $S_1$ is four times that of $S_2$.

Solution

$\mathrm{K} . \mathrm{E} .=\frac{G M m}{2 r}$
$\Rightarrow$ Kinetic energies are unequal
$\begin{aligned}
& \mathrm{T}=\frac{2 \pi r^{3 / 2}}{\sqrt{G M}} \\
& \Rightarrow \text { Time period are equal } \\
& \text {P.E. }=-\frac{G M m}{r} \\
& \Rightarrow \text { Potential energies are unequal } \\
& V=\sqrt{\frac{G M}{r}} \\
& \Rightarrow \text { orbital speeds are equal. }
\end{aligned}$ ~

Asked in: NEET 2007

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