Two satellites of masses $m_{1}$ and $m_{2} (m_{1} > m_{2})$ are revolving round the earth in circular orbits 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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(v_{1} / r_{1}) = (v_{2} / r_{2})

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Solution

The correct option is A $v_{1} < v_{2}$
Velocity of satellite $= \sqrt{\frac{G M}{R + h}}$
Now,
$V_{1} = \sqrt{\frac{G M}{r_{1}}}$
$V_{2} = \sqrt{\frac{G M}{r_{2}}}$
As $r_{1} > r_{2}$
So $V_{1} < V_{2}$

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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 $v_{2}$ ?