Acceleration due to gravity is $g$ on the surface of the earth. The value of acceleration due to gravity at a height of $32 \, km$ above the earth's surface is ........ $g$. (Radius of the earth $= 6400 \, km$)

If the earth were to cease rotating about its own axis,the increase in the value of $g$ in the $C.G.S.$ system at a place of latitude of $45^{\circ}$ will be ........ $cm/sec^{2}$.

Derive the equation for the variation of acceleration due to gravity $g$ with depth $d$ below the surface of the Earth.

Define acceleration due to gravity. Give the magnitude of $g$ on the surface of earth.

Consider two spherical planets of same average density. The second planet is $8$ times as massive as the first planet. The ratio of the acceleration due to gravity of the second planet to that of the first planet is

Given below are two statements:
Statement $I$: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement $II$: Acceleration due to earth's gravity is same at a height '$h$' and depth '$d$' from earth's surface, if $h = d$.
In the light of above statements, choose the most appropriate answer from the options given below.