Question

A man can jump 1.5meter on earth.calculate the approximate height he might be able to jump

Answer 1

Complete 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 -

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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Answer 2

Answer:

Density and radius should be mentioned.

Then this would be the answer.

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