The change in the value of g at a height 'h' above the surface of 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

At height h above the surface of earth.
`g.=g(1-(2h)/(R )) rArr Delta g_(1)=(2h)/(R ).g`
At depth d below the surface of earth
`g.=g(1-(d)/(R )) rArr Delta g_(2)=(d)/(R ).g`
since `Deltag_(1)=Delta g_(2) rArr d=2h`.
So the correct choice is (c ).