Calculate the distance from the surface of the earth at which above the surface, acceleration due to gravity is the same.

Answer

`h=(sqrt(5)-1)/(2)R`

Explanation

Let at height or depth h from surface of earth acceleration due to gravity is same.
`g_(d)=g_(h)`
`g(1-(h)/(R ))=(gR^(2))/((R+h)^(2))rArr ((R-h))/(R )=(R^(2))/((R+h^(2)))`
`(R-h)(R+h)^(2)=R^(3)rArr (R-h)(R^(2)+h^(2)+2hR)=R^(3)`
`R^(3)+Rh^(2)+2hR^(2)-hR^(2)-h^(3)-2h^(2)R=R^(3)rArr h^(2)+Rh-R^(2)=0`
`h = (-R+-sqrt(R^(2)+4R^(2)))/(2) rArr ((sqrt(5)-1)R)/(2)`