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

`g=(4)/(3)pi GRp`
`g'= (4)/(3)pi GRp'`
The gain in P.E. at the highest point will be same in both cases. Hence
`mg'h'= mgh`
`g' =(mgh)/(mg)= (mxx(4)/(3)pi RGph)/(m(4)/(3)piRGp')`
`=(Rph)/(R'p')=(3R'xx4p'xx1.5)/(R'xxp')`
`=18m`.