Two satellites of mass $m_{1}$ and $m_{2} (m_{1} > m_{2})$ revolve round the earth in circular orbits of radii $r_{1}$ and $r_{2}$ respectively $(r_{1} > r_{2})$ Their speeds are related as

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}} = v_{2} r_{2}

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Solution

The correct option is C $v_{1} < v_{2}$
Velocity of a satellite orbiting a radius of $r$ is given by $v = {(\frac{G M}{r})}^{0.5}$
From the given information,
$v_{1} = {(\frac{G M}{r_{1}})}^{0.5}$
$v_{2} = {(\frac{G M}{r_{2}})}^{0.5}$
Take the ratio to compare the velocities i.e.
$\frac{v_{1}}{v_{2}} = {(\frac{G M}{r_{1}})}^{0.5} \times {(\frac{r_{2}}{G M})}^{0.5} = {(\frac{r_{2}}{r_{1}})}^{0.5}$
Given that $r_{2} < r_{1}$ , therefore $v_{1} < v_{2}$ .

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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 $v_{2}$ ?