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

Explanation

We know that in case of Earth
`g=(GM)/(R^(2))=Gxx((4pi//3)R^(3)rho)/(R^(2))=(4/3piG)R rho`
Similarly for the other planet whose radius `R/3 ` and density `(rho)/4 `is `g.((4piG)/3)(R/3)((rho)/4)`
`g.=1/12((4piG)/3)R rho=1/2 g impliesg/(g.)=12`
`h_(max)=(u^(2))/(2g)impliesh_(max)prop 1/g` (here u is constant)
`(h.)/h=g/(g.)=12impliesh.=12h=10xx1.5=18m`