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Question

R and r are the radii of the Earth and the Moon respectively and ρe and ρm are the densities of the Earth and Moon respectively. The ratio of acceleration due to gravity on the surface of the Earth to the Moon is:

A
Rrρeρm
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B
rRρeρm
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C
rRρmρe
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D
Rrρmρe
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Solution

The correct option is A Rrρeρm
Acceleration due to gravity =g=Gm/r2

Also, mass =m=ρV
me=ρe×43πR3
mm=ρm×43πr3

gegm=Gme/R2Gmm/r2=ρeRρmr

Hence correct answer is option A

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