JEE Mains · Physics · STD 11 - 7. gravitation
Two satellites of masses \(m\) and \(3\,m\) revolve around the earth in circular orbits of radii \(r\) and \(3 r\) respectively. The ratio of orbital speeds of the satellites respectively is :
- A \(1: 1\)
- B \(3: 1\)
- C \(\sqrt{3}: 1\)
- D \(9: 1\)
Answer & Solution
Correct Answer
(C) \(\sqrt{3}: 1\)
Step-by-step Solution
Detailed explanation
\(v=\sqrt{\frac{ GM }{ r }}\) \(v \propto \frac{1}{\sqrt{r}} \quad \Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{r_2}{ r _1}}=\sqrt{\frac{3 r}{r}}\) \(=\sqrt{3}: 1\)
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