InterviewSolution
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InterviewSolution
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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 areA. `3/4mgR,(mgR)/6`B. `3/4mgR,(mgR)/12`C. `mgR,mgR`D. `2mgR,mgR` |
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Answer» Correct Answer - B Energy of the skylab in the first orbit is `-(GMm)/(2(2R))=-(GMm)/(4R)` Total energy required to place the skylab into the orbt of radius `2R` frm the surface of earth is `=(GMm)/(4R)-(-(GMm)/R)=(3G/Mm)/(4R)` `=(3gR^(2)m)/(4R)=3/4mgR` Energy of the skylab in the second orbit `=-(GMm)//6R` Energy needed to shift the skylab from the first orbit to the second orbit is `-(GMm)/(4R)-(GMm)/(6R)=(GMm)/Rxx2/24=(mgR)/12` |
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