Two satellites of masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are revolving around the earth in a circular orbit of radii $r_{1}$ and $r_{2}$ $(r_{1} > r_{2})$ , respectively. Which of the following statements is true regarding their speeds $v_{1}$ and $v_{2}$ ?

v_{1} = v_{2}

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v_{1} > v_{2}

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v_{1} < v_{2}

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\frac{v_{1}}{r_{1}} = \frac{v_{2}}{v_{2}}

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Solution

The correct option is B $v_{1} < v_{2}$
Given two satellites of masses $m_{1} & m_{2} (m_{1} > m_{2})$ revolving orbits of radii $r_{1} & r_{2} (r_{1} > r_{2})$
Orbital speed $ν_{o} = \sqrt{\frac{G M_{e}}{r}}$
where $M_{e}$ is mass of earth hence $ν_{0}$ is independent of mass of satellite $m$
$\Rightarrow ν_{0} \propto \frac{1}{\sqrt{r}}$ and since $r_{1} > r_{2} \Rightarrow v_{1} < v_{2}$

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Two satellites of masses $m_{1}$ and $m_{2} (m_{1} > m_{2})$ are revolving round the earth in circular orbits of radius $r_{1}$ and $r_{2} (r_{1} > r_{2})$ respectively. Which of the following statements is true regarding their speeds $v_{1}$ and $v_{2}$ ?