Question

what is the value of g at depth h from surface of earth

Answer 1

Let M is mass and $\rho$ is density of the earth . radius of earth is R.
then, M = $\frac{4}{3}\pi R^3\rho$ [ as you know, mass = volume × density ]

now, acceleration due to gravity at earth's surface is given by,
$g=\frac{GM}{R^2}$

so, $g=\frac{4}{3}\pi R\rho G$..... (1)

and we take a point h depth from the earth's surface then,
$g_h=\frac{4}{3}\pi(R-h)\rho G$.....(2) [ similarly you can treat it ]

dividing equations (2) and (1),
$\frac{g_h}{g}=\frac{R-h}{R}$

hence, $g_h=g\left(1-\frac{h}{R}\right)$