The radius of the Moon is about one-fourth that of the Earth and accel

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

[amp_mcq option1=”10″ option2=”100″ option3=”1,000″ option4=”10,000″ correct=”option2″]

This question was previously asked in

UPSC NDA-1 – 2015

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The acceleration due to gravity (g) on a celestial body with mass M and radius R is given by the formula g = GM/R², where G is the gravitational constant. We are given that the radius of the Moon (Rm) is about one-fourth that of the Earth (Re), i.e., Rm ≈ Re/4. We are also given that the acceleration due to gravity on the Moon (gm) is about one-sixth that on the Earth (ge), i.e., gm ≈ ge/6.
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.

The ratio of masses can be calculated using the relationship between acceleration due to gravity, mass, and radius (g = GM/R²).

The actual ratio of Earth’s mass to Moon’s mass is approximately 81.3, so the given approximate values lead to a result (96) that is closest to 100, indicating the question uses approximate figures typical for simplified calculations.

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