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Question

A geostationary satellite is orbiting in circular orbit. Due to internal forces, suppose the rotating earth automatically shrinks to half the present radius. Assuming mass of the earth remains constant, with respect to a point on equator, now the satellite

A
Will be seen at rest.
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B
Will be seen moving eastward with a period of 8 hours
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C
Will be seen moving westward with a period of 8 hours.
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D
Will be seen moving westward with a period of 6 hours
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Solution

The correct option is C Will be seen moving westward with a period of 8 hours.
The angular momentum of earth will remain conserved. Since moment of inertia will reduce to one fourth, the new angular speed of the earth will become four times the old angular speed ω while the angular speed of the satellite will not change. The relative angular speed will become 3ω and hence, it will take three times less time to complete the cycle with respect to earth. Since, earth moves from west to east, the satellite will be seen to move in opposite direction i.e., westward with time period.
2π3ω=13(2πω)=13(24 hrs)=8 hrs

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