spherical body \(\rho \left( r \right) = \frac{k}{r}\)

\(\frac{M}{V} = \frac{k}{r}\,for\,inside\,r \le R\)

\(M = \frac{{kv}}{r}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\)

Inside the surface of sphere Intensity

\(I = \frac{{GMr}}{{{R^3}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,I = \frac{F}{m}\)

\({g_{inside}} = \frac{{GMr}}{{{R^3}}}\,\,\,\,\,\,\,\,\,\,\,or\,\,\,\,\,\,\,\,\,\,I = \frac{{mg}}{m} = g\)

\( = \frac{G}{{{R^3}}}\frac{{kv}}{r}.r = constant\,\,\,\,\,From\,eq.\,\left( i \right),\)

\(similarly,\,{g_{out}} = \frac{{GM}}{{{r^2}}}\)

Hence, option \((b)\) is correct graph.