JEE Mains · Physics · STD 11 - Gravitation
- JEE Mains 2021
- Hard
- MCQ
Two stars of masses \(m\) and \(2\, m\) at a distance \(d\) rotate about their common centre of mass in free space. The period of revolution is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(2 \pi \sqrt{\frac{ d ^{3}}{3 Gm }}\)
Step-by-step Solution
Detailed explanation
\(F=\frac{G(2 m) m }{ d ^{2}}=(2 m ) \omega^{2}( d / 3)\)
\(\frac{ Gm }{ d ^{2}}=\omega^{2} \frac{ d }{3}\)
\(\Rightarrow \omega^{2}=\frac{3 Gm }{ d ^{3}}\)
\(\Rightarrow \omega=\sqrt{\frac{3 Gm }{ d ^{3}}}\)
\(\Rightarrow T =\frac{2 \pi}{\omega}=2 \pi \sqrt{\frac{ d ^{3}}{3 Gm }}\)
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