Since particle \(C\) is moved without any acceleration,

\(\Rightarrow \Delta K . E =0\)

\(\Rightarrow\) Work done by external agent \(+W_{\text {gravitation }}=0\)

\(\Rightarrow\) Work done by external agent \(=-W g\)

\(=-(-\Delta U)\)

\(=\Delta U\)

\(=U_f-U_{\text {in }}\)

\(U_f=-\frac{G M m}{r}-\frac{G M m}{r}=-\frac{2 G M m}{r}\)

\(U_i=-\frac{G M m}{r / 2}-\frac{G M m}{r / 2}=-\frac{4 G M m}{r}\)

\(\Rightarrow\) Work done \(=\frac{2 G M m}{r}\)