a)In terms of Radius (R) and Mean Density \(\rho\)
we know that \(
g = \frac{{Gm}}
{{R^2 }}
\)
\(
\begin{gathered}
M = \left[ {\frac{4}
{3}\Pi R^3 } \right]\rho \hfill \\
\Rightarrow g = \frac{{G\left[ {\frac{4}
{3}\Pi R^3 \rho } \right]}}
{{R^2 }} \hfill \\
\Rightarrow g = \left[ {\frac{4}
{3}\Pi G} \right]R\rho \hfill \\
\end{gathered}
\)