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A satellite is moving in a circular orbit of radius 3R. Where R is the radius of earth. It is slowly losing energy at a constant rate of α. Then the time after which its orbital radius will be 2R is (Acceleration due to gravity on the surface of earth is g)

a
mgR24α
b
mgR6α
c
mgR8α
d
mgR12α

detailed solution

Correct option is D

Ei=  Initial total energy =-GMm2 x 3R=-GMm6REf= Final total energy =-GMm2 x 2R=-GMm4R∴t=Ei-Efα=1αGMm4R-GMm6R=GMm12αR=mgR12α

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