The ratio of height of a man to the radius of the earth is of the order
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Radius of earth = R
density of earth = p
acceleration due to gravity = g = GM/ R²
M= 4/3 λ R³p
so, g = 4/3G λ Rp
acceleration due to gravity on planet
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
the height through which a man can jump on the planet = h'
g/g' = h/h'
12= h'/ 1.5
h'= 18m
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