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Question

The magnitude of gravitational potential energy of earth-moon systems is U which are zero at infinite separation, If K is the K.E. of the moon with respect to earth, then

A
|U|=K
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B
|U|<K
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C
|U|>K
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D
Either B or C
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Solution

The correct option is D |U|>K
The orbital velocity of moon is
v0m=GMer
.................(i)
So kinetic energy of moon is K=1/2Mmv20m
K=GMeMm2r.................(ii)
U=GMeMmr.................(iii)
where r is distance between the centres of earth & moon
Hence |U|>K

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