The gravitational field due to a
spherical shell of matter (or equivalently, the electric field due
to a spherical shell of charge) is given by:

\begin{equation}
\Vec g =
 \begin{cases}
		0&\textrm{for } r<a\\
		-G \,\frac{M}{b^3-a^3}\,
 \left( r-\frac{a^3}{r^2}\right)\, \hat r & \textrm{for } a<r<b\\
		-G\,\frac{M}{r^2}\, \hat r & \textrm{for } r>b \\
	\end{cases}
\end{equation}
(If you want extra practice with Gauss's law, this is a good question to practice on!)

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%*{{homework:figures:vfmass0.png?300|Figure: a spherical shell of matter}}

This problem explores the consequences of the divergence
theorem for this shell.