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

The acceleration due to gravity (g) on a celestial body is given by the formula g = GM/R", where G is the universal gravitational constant, M is the mass, and R is the radius. According to the question, the radius of the Moon (Rm) is approximately 1/4 of the Earth's radius (Re), and the acceleration due to gravity on the Moon (gm) is 1/6 of that on Earth (ge) [3]. Rearranging the formula for mass, M = (g!! R") / G. Therefore, the ratio of the mass of Earth (Me) to the mass of the Moon (Mm) is calculated as (ge / gm)!! (Re / Rm)". Substituting the given values: Me/Mm = (6)!! (4)" = 6!! 16 = 96. This value is approximately 100, making option 2 the correct choice.

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 2: The Solar System > Moon > p. 28
2. [2] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > Prepare some questions based on your learnings so far ... > p. 78
3. [3] https://en.wikipedia.org/wiki/Gravitation_of_the_Moon