Two satellites of masses m and 3m revolve around the earth in circular orbits of radii and respectively. The ratio of orbital speeds of the satellites respectively is [2023]

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Solution

Q.
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 [2023]

1 1 : 1

2 3 : 1

3 $\sqrt{3}$ : 1

4 9 : 1

Ans.
(3)

$v = \sqrt{\frac{G M}{r}}$

$v \propto \frac{1}{\sqrt{r}}$

$\Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{r_{2}}{r_{1}}} = \sqrt{\frac{3 r}{r}} = \sqrt{3} : 1$

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