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Question

A satellite of mass m is revolving in circular orbit of radius r around the earth. Its angular momentum w.r.t. the centre of its orbit is(M= mass of earth, G = universal gravitational constant)

A
(GMmr)1/2
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B
(GMm2r)1/2
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C
(GMm2r2)1/2
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D
(GM2m2r)1/2
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Solution

The correct option is C (GMm2r)1/2Let 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 earth.∴ Fcentripetal=Fgravitational⇒mv2r=GMmr2 ⇒v=√GMrAngular momentum of satellite about the centre of orbit, L=mvrL=m(GMr)1/2r⟹ L=(GMm2r)1/2

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