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Artificial satellites - class-VIII
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A satellite of mass $m$ revolving around the earth in a circular orbit of radius $2R$ has to be shifted to another circular orbit of radius $4R$. The energy required for this process will be ($M\rightarrow$ mass of earth, $R\rightarrow$ radius of the earth)
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A
$\dfrac {GMm}{8R}$
💡 Explanation:
The total energy of a satellite in an orbit of radius r is E = -GMm / (2r). The energy required to move from 2R to 4R is E2 - E1 = (-GMm / 8R) - (-GMm / 4R) = (-GMm + 2GMm) / 8R = GMm / 8R.