d
(d) \(g = \frac{4}{3}\pi \rho Gr\)
\(g \propto r \) if \(r < R\)
\(g = \frac{{GM}}{{{r^2}}}\)
\(g \propto \frac{1}{{{r^2}}}\) if \(r > R\)
If \({r_1} < R\) and \({r_2} < R\) then \(\frac{{{F_1}}}{{{F_2}}} = \frac{{{g_1}}}{{{g_2}}} = \frac{{{r_1}}}{{{r_2}}}\)
If \({r_1} > R\) and \({r_2} > R\) then \(\frac{{{F_1}}}{{{F_2}}} = \frac{{{g_1}}}{{{g_2}}} = {\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^2}\)