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.
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Let Radius of earth = R
and density of earth = p
Acceleration due to gravity = g = GM/ R²
Now, M= 4/3 λ R³p
=> g = 4/3G λ Rp
We know that,
g' = G'M'/ R'²
or g' = 4/3 G'λR'p'
p' = 1/4p
R' = 1/3 R
g' = 1/12(4/3 GλRp)
g' = 1/12g
Let the height through which a man can jump on the planet = he
g/g' = h/he
=> 12= he / 1.5
=> he = 18m
and density of earth = p
Acceleration due to gravity = g = GM/ R²
Now, M= 4/3 λ R³p
=> g = 4/3G λ Rp
We know that,
g' = G'M'/ R'²
or g' = 4/3 G'λR'p'
p' = 1/4p
R' = 1/3 R
g' = 1/12(4/3 GλRp)
g' = 1/12g
Let the height through which a man can jump on the planet = he
g/g' = h/he
=> 12= he / 1.5
=> he = 18m
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