Question

if the mass of earth is 100 times that of the moon and radius of the earth is 4times that of the moon. prove that the acceleration due to gravity on moon is 1/6 of the earth.​

Answer 1

Given:-

•Mass of the earth is 100 times that of the moon

•Radius of the earth is 4 times that of moon.

To prove:-

•Acceleration due to gravity on moon(gm) is 1/6 of that of acceleration due to gravity on the earth(ge).

Solution:-

We know that:-

=>g=GM/R²

To find 'g' on earth:-

=>ge=GMe/R²e

To find 'g' on moon:-

=>gm=GMm/R²m

So,ratio of acceleration due to gravity on moon to that of earth is:-

=>gm/ge=GMm/R²m×R²e/GMe

=>gm/ge=Mm/Me×(Re/Rm)²

=>gm/ge=Mm/100Mm×(4Rm/Rm)²

=>gm/ge=16/100

=>gm/ge=1/6 (approximately)

Hence, proved that acceleration due to gravity on the moon is 1/6 of the earth.