Two planets $A$ and $B$ of equal mass are having their period of revolutions $T_{A}$ and $T_{B}$ such that $T_{A}=2 T_{B}$. These planets are revolving in the circular orbits of radii $I_{A}$ and $I_{B}$ respectively. Which out of the following would be the correct relationship of their orbits?
Two planets $A$ and $B$ of equal mass are having their period of revolutions $T_{A}$ and $T_{B}$ such that $T_{A}=2 T_{B}$. These planets are revolving in the circular orbits of radii $I_{A}$ and $I_{B}$ respectively. Which out of the following would be the correct relationship of their orbits?
- [JEE MAIN 2022]
- A
$2 r_{A}^{2}=r_{B}^{2}$
- B
$r_{A}^{3}=2 r_{B}^{3}$
- C
$r _{ A }^{3}=4 r _{ B }^{3}$
- D
$T_{A}^{2}-T_{B}^{2}=\frac{\pi^{2}}{G M}\left(r_{B}^{3}-4 r_{A}^{3}\right)$
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- [AIIMS 1995]
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