Question

A man can jump 1.5m high on earth. Calculate the height he might be able jo jump on a planet whose density is 1/4 that of the earth and whose radius is 1/3 of that of the earth?

Answer 1

g ∝ R ρ

g’ / g = (R’ / R) × (ρ’ / ρ)

g’ = g × (R’ / R) × (ρ’ / ρ)

g’ = g × (R / (3R)) × (ρ / (4 ρ))

g’ = g / 12

Acceleration due to gravity of that planet is g / 12

H ∝ 1 / g

H / H’ = g’ / g

H’ = H × (g / g’)

H’ = 1.5 × (g / (g/12))

H’ = 18 m

He can jump 18 m on that planet.

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Answer 2

acceleration due to gravity on planet
g' = G'M'/ R'²
or g' = 4/3 G'λR'd'
d' = 1/4p
R' = 1/3 R
g' = 1/12(4/3 GλRd)
g' = 1/12g
the height which man can jump on the planet = h'
g/g' = h/h'
12= h'/ 1.5
h'= 18m