The ratio of radii of earth to another planet is `2//3` and the ratio of their mean densities is `4//5` if an astronaut can jump to a maximum height of 1.5 m on the earth with the same effort the maximum height he can jump on that planet is

Options

A. 1m
B. 0.75 m
C. 0.5 m
D. 1.25 m

Answer

B

Explanation

Given `(R_(e))/(R_(p))=2/3,(d_(e ))/(d_(p))=4/5`
as `MG=gR_(e)^(2)` and `M=d_(e )xx4/3piR_(e)^(3)`
por `d_(e )xx4/3 piR_(e )xxG=g_(e )`
similarly for planet `d_(p)xx4/3piR_(p)G=g_(p)`
Dividing Eq I by Eq ii we get
`(g_(e ))/(g_(p))=(R_(e))/(R_(p))xx(d_(e ))/(d_(p))`
`=2/3xx4/5=8/15=0.5`
`g_(p)=(g_(e ))/(0.5)=2g_(e )`
but we know that E=Mgh
`2geh_(p)=gexx1.5`
`h_(e )=1.5/2=0.75 m`