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:

  1.  v equals fraction numerator G M over denominator r end fraction
  2.  V squared equals fraction numerator G M m over denominator r end fraction
  3.  V squared equals fraction numerator G M over denominator r end fraction
  4.  V squared equals g M over r

hintHint:

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


    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 m v squared over denominator r end fraction =fraction numerator G M m over denominator r squared end fraction
    After solving, we get:
    v2fraction numerator G M over denominator r end fraction

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