Choose the correct alternative:
$(a)$ Acceleration due to gravity increases/decreases with increasing altitude.
$(b)$ Acceleration due to gravity increases/decreases with increasing depth (assume the Earth to be a sphere of uniform density).
$(c)$ Acceleration due to gravity is independent of mass of the Earth/mass of the body.
$(d)$ The formula $-G M m(1 / r_{2}-1 / r_{1})$ is more/less accurate than the formula $m g(r_{2}-r_{1})$ for the difference of potential energy between two points $r_{2}$ and $r_{1}$ distance away from the centre of the Earth.

(A) Decreases,$(b)$ Decreases,$(c)$ Mass of the body,$(d)$ More.
$(a)$ Acceleration due to gravity at height $h$ is $g_{h} = g(1 - 2h/R_{e})$. Thus,it decreases with increasing altitude.
$(b)$ Acceleration due to gravity at depth $d$ is $g_{d} = g(1 - d/R_{e})$. Thus,it decreases with increasing depth.
$(c)$ Since $g = GM/R^{2}$,the acceleration due to gravity is independent of the mass of the body $(m)$.
$(d)$ The potential energy difference is $\Delta U = -GmM(1/r_{2} - 1/r_{1})$. The formula $mg(r_{2}-r_{1})$ is only an approximation for small distances near the surface. Thus,the former is more accurate.