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Q70 (NDA-I/2015) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Astronomy and astrophysics Answer Verified

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

Result
Your answer: —  Â·  Correct: B
Explanation

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
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