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MHT CET20226 Aug 2022Morning ShiftPhysicsGravitationActual

A satellite of mass m is moving in a circular orbit of radius r around the earth. The angular momentum of the satellite about the center of orbitis ( M= mass of earth, G= gravitational constant)

Options

  1. A(G M m^2 r^2 )^ 1 / 2
  2. B(G M m r)
  3. C(G M m^2 r )^ 1 / 2
  4. D(G M^2 m r )^ 1 / 2

Correct answer

C. (G M m^2 r )^ 1 / 2

Step-by-step solution

Let the satellite revolves in a circular orbit of radius r with a linear velocity v . The centripetal force of acting on the satellite is balanced by the gravitational force due to the earth. aligned & F_ centripetal =F_ gravitational & m v^2 r = G M m r^2 & v= G M r aligned Angular momentum of satellite about the center of orbit, is L=m v r=m ( G M r )^ 1 / 2 r= (G M m^2 r )^ 1 / 2

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