Explanation:

(a) Acceleration due to gravity decreases with increasing altitude.

$\mathrm{The} \mathrm{relation} \mathrm{between} \mathrm{the} \mathrm{two} \mathrm{is} \mathrm{given} \mathrm{by} :$
${\mathrm{g}}_h=\left(1-\frac{2\mathrm{h}}{{\mathrm{R}}_{\mathrm{e}}}\right)\mathrm{g}$
$\mathrm{Where},$
$R_e =radius of the earth$
$g=acceleration due to gravity on the surface of earth$

It is clear from the given relation that acceleration due to gravity decreases with an increase in height.

(b) Acceleration due to gravity at depth d is given by the relation:

${\mathrm{g}}_{\mathrm{d}}=\left(1-\frac{\mathrm{d}}{{\mathrm{R}}_{\mathrm{e}}}\right)\mathrm{g}$

It is clear from the given relation that acceleration due to gravity decreases with an increase in depth.

(c) Acceleration due to gravity of the body of mass m is given by the relation:

$\mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2}$

Where,

G = Universal gravitational constant

M = Mass of the Earth

R = Radius of the Earth Hence, it can be inferred that acceleration due to gravity is independent of the mass of the body.

(d) The gravitational potential energy of two points ${\mathrm{r}}_2$ and ${\mathrm{r}}_1$ distance away from the centre of the Earth is respectively given by:

$\mathrm{V}\left({\mathrm{r}}_1\right)=-\frac{\mathrm{GmM}}{{\mathrm{r}}_1}$
$\mathrm{V}\left({\mathrm{r}}_2\right)=-\frac{\mathrm{GmM}}{{\mathrm{r}}_2}$

$So,$Difference in potential energy, $=\mathrm{V}\left({\mathrm{r}}_2\right)-\mathrm{V}\left({\mathrm{r}}_1\right)=-\mathrm{GmM}\left(\frac{1}{{\mathrm{r}}_2}=\frac{1}{{\mathrm{r}}_1}\right)$

Hence, this formula is more accurate than the formula mg $({\mathrm{r}}_2– {\mathrm{r}}_1).$