Physics
Grade-10
Easy
Question
The radius of the orbit is r, for a satellite of mass m, which is moving around a planet of mass M, then the orbital velocity of the satellite is given by:
Hint:
On a body in circular motion, gravitational force of attraction and centripetal forces act.
The correct answer is: ![V squared equals fraction numerator G M over denominator r end fraction](data:image/png;base64,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)
Mass of planet = M
Mass of satellite = m
Radius of orbit = r
Let, v be the velocity of the satellite. For the satellite to be able to revolve in the orbit, the centripetal force must be balanced by gravitational force
Fc = Fg
=![fraction numerator G M m over denominator r squared end fraction](data:image/png;base64,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)
After solving, we get:
v2 = ![fraction numerator G M over denominator r end fraction](data:image/png;base64,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)
Let, v be the velocity of the satellite. For the satellite to be able to revolve in the orbit, the centripetal force must be balanced by gravitational force
Fc = Fg
After solving, we get:
v2 =
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