JEE Mains · Physics · STD 11 - 7. gravitation
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?
- 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 \(T_{A}^{2}-T_{B}^{2}=\frac{\pi^{2}}{G M}\left(r_{B}^{3}-4 r_{A}^{3}\right)\)
Answer & Solution
Correct Answer
(C) \(r _{ A }^{3}=4 r _{ B }^{3}\)
Step-by-step Solution
Detailed explanation
\(T =\frac{2 \pi}{\sqrt{ Gm _{ A }}} r ^{\frac{3}{2}}\) \(T ^{2} \propto r ^{3}\) \(\left(\frac{ T _{ A }}{ T _{ B }}\right)^{2}=\left(\frac{ r _{ A }}{ r _{ B }}\right)^{3}\)…
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