Two satellites of masses $m_{1}$ and $m_{2} (m_{1} > m_{2})$ are revolving round the earh in circular orbits of radii $r_{1}$ and $r_{2} (r_{1} > r_{2})$ respectively. Which of the following statements are true regarding their velocities $v_{1}$ 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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(v_{1} / r_{2}) = (v_{2} / r_{2})

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Solution

The correct option is B $v_{1} < v_{2}$
Since $v ($ orbital velocity $) = \sqrt{\frac{G M}{r}}$
So $\frac{v_{1}}{v_{2}} = \sqrt{\frac{r_{2}}{r_{1}}} \Rightarrow v_{1} < v_{2} (∵ r_{1} > r_{2})$

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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 $v_{2}$ ?