If 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 it (both `h` and `d` are much smaller than the radius of the earth), then

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. `g'=g(1-(2h)/R)rArr Deltag_1=(2h)/R g`
At depth d below the surface of the earth, `g'=g(1-d/R)rArr Deltag_2=d/R g`
Since `Deltag_1=Deltag_2 , d=2h`