A person can jump maximum up to 20 meters on the surface of the earth. Find the maximum height to which he can jump on the surface of a planet having mass 2/3 times and radius 4/3 times the radius of earth
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Answer: Let R,ρ be the radius and density of
Earth. The acceleration due to gravity on Earth is
g=GMR2=GR2×43πR3ρ=43πGRρ
The acceleration due to gravity on planet is
g'=43πGR'ρ'=43πG(R/3)(ρ/4)
=12×43πGRρ=g12
Assume that the man puts the same energy in jumping high on Earth surface and on the planet surface, then
mgh=mg'h' or h'=gg'h=gg/12h=12h
=12×2=24m
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