At what height above the surface of the earth is the gravitational potential energy of a body equal to that on the surface of the moon ? Assume that the mass of the earth is 80 times that of the moon and the radius of the earth is 4 times that of the moon. Given ,Radius of the earth =6400 km.

Explanation

Mass of the earth =M , mass of the moon =`M/(80)`
Radius of the earth , R=6400km and radius of the moon `=R/4`
Gravitational potential energy of a body of mass m at a distance r from the centre of the earth `=-(GMm)/r`
Again, gravitational potential energy on surface of the moon
`=-(G*M/(80)*m)/(R/4)=(GMm)/(20R)`
Now, `-(GMm)/r=-(GMm)/(20R) or, r=20R`
So, height above the surface of the earth
`=r-R=20R-R=19R=19xx6400`
=121600 km