Question

I will be thank full to u if u help me in solving the below problem
If the change in the value of g at a height h above the surface of the earth is same as depth x below the surface of the earth, then (h<<R)

Answer 1

If the two values of g' are equal, and we let g be the value of the acceleration of gravity at the Earth's surface,

g*R^2/(R+h)^2 = g*(R-x)/R

because g' is proportional to distance from the center of the earth, below the surface, if the earth has constant density

R^3 = (R-x)*(R+h)^2

1 = (1- x/R)(1 + h/R)^2
= 1 + (2h/R) +h^2/R^2 -(x/R)[1 + (2h/R) +h^2/R^2]
= 1 + 2h/R -x/R + higher order terms
2h/R = x/R + higher order terms (neglect them)
x = 2h

Answer 2

Solve for the values of U and V below?