JEE Mains · Physics · STD 11 - Gravitation
- JEE Mains 2022
- Medium
- MCQ
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?
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(r _{ A }^{3}=4 r _{ B }^{3}\)
Step-by-step Solution
Detailed explanation
\(T =\frac{2 \pi}{\sqrt{ Gm _{ A }}} r ^{\frac{3}{2}}\)
\(T ^{2} \propto r ^{3}\)
\(\left(\frac{ T _{ A }}{ T _{ B }}\right)^{2}=\left(\frac{ r _{ A }}{ r _{ B }}\right)^{3}\)
\(\Rightarrow\left(\frac{2}{1}\right)^{2}=\left(\frac{ r _{ A }}{ r _{ B }}\right)^{3} \Rightarrow r _{ A }^{3}=4 r _{ B }^{3}\)
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