The mass of the moon is 1/144 times the mass of a planet and its diameter is 1/16 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be :

Solution

Physics sir · 4 steps

Escape velocity goes as √(M/R), so take the ratio and let G and the 2 cancel.

1. Formula. Escape velocity from the surface of a body of mass M and radius R depends only on M/R.

   vₑ = √(2GM/R) ⇒ vₘ/vₚ = √(Mₘ/Mₚ × Rₚ/Rₘ)

2. Diameter to radius. The radius is half the diameter for both bodies, so the ratio of radii equals the ratio of diameters: Rₘ/Rₚ = 1/16, which means Rₚ/Rₘ = 16.
3. Put in numbers. vₘ/vₚ = √(1/144 × 16) = √(16/144) = √(1/9) = 1/3.
4. So. The escape velocity on the moon is v/3, option (d).

The idea to keep. For escape velocity comparisons, remember vₑ ∝ √(M/R). A smaller mass lowers it, but a smaller radius raises it, so always use both ratios together.

Answer from the NTA final answer key. Solution by PrepWiser.