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?

A
Satellite #1, by a factor of 2
B
Satellite #1, by a factor of 2
C
Satellite #2, by a factor of 2
D
Satellite #2, by a factor of 2
E
Neither; the satellite's speeds are the same

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 earthfor 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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