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?

Explanation

At height h, `g_h = g (1 - (2h)/(R ))` where h < < R
or ` g -g_h =(2hg)/( R) " or " Delta_(g_h) = (2hg)/(R ) ` ….(i)
At depth d, `g_d = g (1 - d/R) ` where d < < R
or `g -g_d = (dg)/( R)`
or `Delta_(g_d) =(dg)/(R )` ...(ii)
Form (i) and (ii) , when `Delta_(g_h) = Delta_(g_d)`
From (i) and (ii), when `Delta_(g_h) = Delta_(g_d)`
`(2hg)/(R ) - (dg)/(R ) " or " d = 2h`