The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth,assumed to be a sphere of radius $R$ of uniform density,is as shown in the figure below. The correct figure is:

$A$ spherical planet has a mass $M$ and diameter $D$. $A$ particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity equal to:

The height $h$ above the earth's surface at which the value of acceleration due to gravity $g$ becomes $\frac{g}{3}$ is ($R=$ radius of the earth).

The value of $g$ at a particular point is $9.8\,m/s^2$. Suppose the Earth suddenly shrinks uniformly to half its present size without losing any mass. The value of $g$ at the same point (assuming that the distance of the point from the centre of the Earth does not shrink) will now be ......... $m/s^2$.

The masses of two planets are in the ratio $1 : 2$. Their radii are in the ratio $1 : 2$. The ratio of the acceleration due to gravity on the planets is:

Obtain an expression for the acceleration due to gravity of the Earth at a depth $d$ below its surface.