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Q.

A skylab of mass m kg is first launched from the surface of the earth in a circular orbit of radius 2R (from the centre of the earth) and then it is shifted from this circular orbit to another circular orbit of radius 3R. The minimum energy required to place the lab in the first orbit and to shift the lab from first orbit to the second orbit are

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a

34mgR,mgR6

b

34mgR,mgR12

c

mgR,mgR

d

2mgR,mgR

answer is B.

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Detailed Solution

Energy of the skylab in the first orbit is−GMm2(2R)=−GMm4RTotal energy required to place the skylab into the orbit of radius 2R from the surface of earth is−GMm4R−−GMmR=3GMm4R=3gR2m4R=34mgREnergy of the skylab in the second orbit =−(GMm)/6REnergy needed to shift the skylab from the first orbit to thesecond orbit is−GMm4R−GMm6R=GMmR×224=mgR12

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