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

Acceleration due to gravity at height h
`G_(h)=g(1-(2h)/(R ))`
and depth d `g_(d)=g(1-(d)/(h))`
from eqs I and ii we get
`g(1-(2h)/(R ))=g(1-(d)/(R ))`
`rarr 2h=d`