The gravitational force between a hollow spherical shell (of radius $R$ and uniform density) and a point mass $m$ is $F$. Show the nature of the $F$ versus $r$ graph,where $r$ is the distance of the point mass from the centre of the hollow spherical shell.

(N/A) According to the shell theorem for gravitation:
$1$. For a point mass $m$ located outside the hollow spherical shell $(r \geq R)$,the shell acts as if all its mass $M$ is concentrated at its centre. Thus,the gravitational force is given by $F = \frac{GMm}{r^2}$.
$2$. For a point mass $m$ located inside the hollow spherical shell $(r < R)$,the net gravitational force exerted by the shell on the point mass is zero,because the gravitational fields from different parts of the shell cancel each other out. Thus,$F = 0$.
The graph of $F$ versus $r$ is zero for $0 \leq r < R$ and follows an inverse-square law $(F \propto 1/r^2)$ for $r \geq R$.