c
\({F_{PA}} = \)\(A = \frac{{Gmm}}{{{x^2}}} = F\)

\({F_{PB}} = \frac{{G2mm}}{{{x^2}}} = 2F\), \({F_{PC}} = \frac{{G3mm}}{{{x^2}}} = 3F\) ,\({F_{PD}} = \frac{{G4mm}}{{{x^2}}} = 4F\)

\({\overrightarrow F _{net}} = {\overrightarrow F _{PA}} + {\overrightarrow F _{PB}} + {\overrightarrow F _{PC}} + {\overrightarrow F _{PD}} = 2\sqrt 2 \,F\)

\(\therefore {\overrightarrow F _{net}} = 2\sqrt 2 \frac{{Gmm}}{{{x^2}}}\)

\( = 2\sqrt 2 \frac{{G{m^2}}}{{{{(a/\sqrt 2 )}^2}}}\)    [\(x = \frac{a}{{\sqrt 2 }} = \)]

\( = \frac{{4\sqrt 2 \,G{m^2}}}{{{a^2}}}\)