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Satellites

Two artificia...

Question

Two artificial satellite 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 speed $v_{1}$ and $v_{2}$ ?

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 C $v_{1} < v_{2}$
Answer is C.

Orbital velocity is the velocity given to the body to keep it in orbit. This velocity is usually given to the artificial satellite so that it revolves round any particular planet. It is given by $V_{o r b i t} = \sqrt{\frac{G M}{R}}$ .
where,
$G$ is gravitational constant,
$M$ is the mass of the body at center,
$R$ is radius of orbit.
Therefore, the velocity of the satellite does not depend on the mass of the satellite but inversely proportional to the radius of the orbit. So, $v_{1} < v_{2}$ .

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