Q111 / 200 · NEET 2007 · Physics

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?

  • A
    The potential energies of earth and satellite in the two cases are equal.
  • Correct answer
    B
    $S_1$ and $S_2$ are moving with the same speed
  • C
    The kinetic energies of the two satellites are equal
  • D
    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 $\begin{aligned} & \mathrm{T}=\frac{2 \pi r^{3 / 2}}{\sqrt{G M}} \\ & \Rightarrow \text { Time period are equal } \\ & \text {P.E. }=-\frac{G M m}{r} \\ & \Rightarrow \text { Potential energies are unequal } \\ & V=\sqrt{\frac{G M}{r}} \\ & \Rightarrow \text { orbital speeds are equal. } \end{aligned}$

Hence, the correct answer is option: 'B'.

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