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An object is projected vertically upward...

An object is projected vertically upward from the surface of the earth at which above and below the surface acceleration due to gravity is the same.

Text Solution

Verified by Experts

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