The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?

Options

A. `d=(h)/(2)`
B. `d=(3h)/(2)`
C. `d=2h`
D. `d=h`

Answer

C

Explanation

`g_(h)=g((1-2h)/(R)),g_(d)=g(1-(d)/(R))`
`Deltag_(h)=Deltag_(d)impliesg((2h)/(R))=g((d)/(R))implies2h=d`