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Satellites

Two artificia...

Question

Two artificial satellites of masses $m_{1}$ and $m_{2}$ are moving with speeds $v_{1}$ and $v_{2}$ in orbits of radii $r_{1}$ and $r_{2}$ respectively. If $r_{1} > r_{2}$ then which of the following statements is true.

A

$v_{1} < v_{2}$

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B

$v_{1} = v_{2}$

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C

$v_{1} > v_{2}$

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D

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

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Solution

The correct option is A
$v_{1} < v_{2}$

Orbital velocity is given by the formula: $v = \sqrt{\frac{G M}{r}}$ .Here $G$ is the gravitational constant, $M$ is mass of planet, and $r$ is the radius.
Orbital velocity is inversely proportional to the square root of radius.
So, $r_{1} > r_{2}$ then $v_{1} < v_{2}$ .
Hence, option (A) is correct.

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