The radius of the Moon is about one-fourth that of the Earth and acceleration due to gravity on the Moon is about one-sixth that on the Earth. From this, we can conclude that the ratio of the mass of Earth to the mass of the Moon is about
10
100
1,000
10,000
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-1 – 2015
From g = GM/R², we can write M = gR²/G.
The ratio of the mass of Earth (Me) to the mass of the Moon (Mm) is:
Me/Mm = (ge * Re² / G) / (gm * Rm² / G)
Me/Mm = (ge/gm) * (Re/Rm)²
Substitute the given ratios: ge/gm ≈ 6 and Re/Rm ≈ 4.
Me/Mm ≈ 6 * (4)² = 6 * 16 = 96.
Among the options, 96 is closest to 100.