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. `x=h`
B. `x=2h`
C. `x=h/2`
D. `x=h^(2)`

Answer

B

Explanation

The value of g at the height h form the surface of earth
`g'=g(1-(2h)/R)`
The value of `g` at depth `x` below the surface of earth
`g'=g(1-x/R)`
These two are given equal, hence ` (1-(2h)/R)=(1-x/R)`
On solving, we get `x=2h`