A man can jump 1 5 m high on the earth Calculate the approximate height he might be able - Physics - Gravitation

Question

A man can jump 1 5 m high on the earth Calculate the
approximate height he might be able to jump on a planet whose
density is one-quarter of the earth and the radius is one-third of
the earthâ€™s radius

Hansraj Rai · Accepted Answer

Let the radius and density of the earth be R and ρ respectively.

Acceleration due to gravity on surface of the earth is,

$g = \frac{G M}{R^{2}} M = \frac{4}{3} π R^{3} ρ g = \frac{4}{3} G π R ρ$

Acceleration due to gravity on the planet,

$g' = \frac{G M'}{{R'}^{2}} M' = \frac{4}{3} π {R'}^{3} ρ' g' = \frac{4}{3} G π R' ρ' ρ' = \frac{1}{4} ρ a n d R' = \frac{1}{3} R g' = \frac{1}{12} (\frac{4}{3} G π R ρ) = \frac{1}{12} g$

Let h' be the up to that man can jump on the planet, so

$\frac{g}{g'} = \frac{h'}{h} 12 = \frac{h'}{1.5} h' = 18 m$

A man can jump 1.5 m high on the earth. Calculate the approximate height he might be able to jump on a planet whose density is one-quarter of the earth and the radius is one-third of the earth’s radius.