Question

A man can jump 2m high on earth . What is the approximate heigh he might be able to jump on a planet whose density is one quarter that of earth and radius is one third that of earth.

Answer 1

g = GM/R²
g = GVρ/R²
g = 4/3 * (GπR³ρ) / R²
g = 4GRπρ/3
g is directly proportional to Rρ

g₁/g₂ = (R₁/R₂) × (ρ₁/ρ₂)
g/g’ = (3R/R) × (4ρ/ρ)
g/g’ = 12
g’ = g/12

E = mgh
With energy and mass being constant
h is inversely proportional to g
h₁/h₂ = g₂/g₁
h₂ = h₁ × (g₁/g₂)
h₂ = 2 × (12g/g)
h₂ = 24m

He can jump 24m on that planet.