A satellite can be in a geostationary orbit around earth at a distance r from the centre. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth if its distance from the centre is :-
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Question

A satellite can be in a geostationary orbit around earth at a distance r from the centre. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth if its distance from the centre is :-

Options

G1 Physics · Accepted Answer

For a geostationary satellite, ω²r³ = GM, so r ∝ ω⁻²ᐟ³. If Earth's angular speed doubles, r′/r = 2⁻²ᐟ³ = 4⁻¹ᐟ³. Hence r′ = r/4¹ᐟ³. Correct answer: C.