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Question

The mass of satellite 2 is twice the mass of satellite 1. Both the satellites are revolving the earth at a constant speed in circular orbits at a constant speed. Which satellite's speed is greater?
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A
Satellite #1, by a factor of 2
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B
Satellite #1, by a factor of 2
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C
Satellite #2, by a factor of 2
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D
Satellite #2, by a factor of 2
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E
Neither; the satellite's speeds are the same
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Solution

The correct option is B Satellite #1, by a factor of $$\sqrt{2}$$
The speed of a satellite is given by $${v}_{o}=\sqrt{\dfrac{GM}{r}}$$
where M is mass of earth
for satellite 2     $${v}_{o}=\sqrt{\dfrac{GM}{2r}}$$
for satellite 1      $${v'}_{o}=\sqrt{\dfrac{GM}{r}}$$
now by dividing the speed of satellite 1 by the speed of satellite 2
           
             $${v'}_{o}=\sqrt{2}{v}_{o}$$
it is clear that speed of satellite 1 is greater than satellite 2 by a factor of $$\sqrt{2}$$ 
the note-orbital velocity of a satellite does not depend upon its mass.           

Physics

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