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 then 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

At height `h` above the surface of the earth, therefore
`g'=G(1-(2h)/R)implies/_\g_(1)=(2h)/Rg`
At depth `d` below the surface of the earth
`g'=g(1-d/R)implies/_\g_(2)=d/Rg`
`/_\g_(1)=/_\g_(2)impliesd=2h`