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Q.

What is the radius of the circular orbit of a stationary satellite which remains motionless with respect to earth’s surface ?

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a

gR2T24π213

b

gR4π2T212

c

gRT2π13

d

gR2πT12

answer is A.

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Detailed Solution

A satellite will appear motionless when its period of revolution is the same as that of earth that is T=24 hours. Let r be the radius of orbit from the centre of earth. Then dynamics of circular motionmω2r=GMmr2 ; 2πT2r3=GMr=GMT24π213=gR2T24π213∵GM=gR2

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