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 earth’s radius.

Answer 1

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

Answer 2

Answer:

18m

Explanation:

M=4/3∆R^3P

so. g=4/3∆RP

Acceleration due to gravity

g' = G'∆/R'^2

= 4/3G'∆R'P'

P'=1/4P

R' =1/3R

g'= 1/12 ( 4/3 G'∆R'P' )

g'= 1/12g

the height through which a man can jump = h'

g/g' = h/h'

12. =. h'/1.5

h= 18m