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Question

The minimum work that has to be performed to bring a spaceship of mass m=2.0×103kg from the surface of the Earth to the Moon is 1.38×10n J where n is:

Solution
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Potential energy at surface of earth =Ue=GMemRe

And, g=GMR2

Ue=mgeRe where ge=g at surface of earth

Ue=2×103×9.8×6.4×106=1.4×1011J

At moon, =Um=GMmmRm=6.67×1011×7.35×1022×2×1031.76×106=5.6×109J

Work done=W=UmUe1.4×1011J

Hence, n=11

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