\begin{problem*}{1.10}
Newton's law of universal gravitation is represented by
\begin{equation}
F = \frac{GMm}{r^2}
\end{equation}
where $F$ is the magnitude of the gravitational force exerted by one
small object on another, $M$ and $m$ are the masses of the objects,
and $r$ is a distance.  Force has the SI units
$\bareU{kg$\cdot$m/s$^2$}$.  What are the SI units of the
proportionality constant $G$?
\end{problem*} % Probem 1.10

\begin{solution}
\begin{align}
  F &= \frac{GMm}{r^2} \\
  \bareU{kg$\cdot$m/s$^2$} &= G\frac{\bareU{kg$^2$}}{\bareU{m$^2$}} \\
  G &= \ans{\bareU{m$^3$/kg$\cdot$s$^2$}}
\end{align}
\end{solution}
