Find the acceleration due to gravity of the Moon at a point $1000 \mathrm{km}$ above the Moon's surface.

The mass of the Moon is $7.4\times {10}^{22} \mathrm{kg}$ and its radius is $1740 \mathrm{km}$.

A solid sphere of mass $m$ and radius $r$ is placed inside a hollow thin spherical shell of mass $M$ and radius $R$ as shown. A particle of mass $m^{\text{'}}$ is placed on the line joining the two centres at a distance $x$ from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if

$\left(a\right)$ $r<x<2 r$

$\left(b\right)$ $2 r<x<2 R$

$\left(c\right)$ $x>2 R$