c
Initial gravitational potential energy,

\({E_i} =  - \frac{{GMm}}{{2R}}\)

Final gravitational potential energy,

\({E_f} =  - \frac{{GMm/2}}{{2\left( {\frac{R}{2}} \right)}}\frac{{GMm/2}}{{2\left( {\frac{{3R}}{2}} \right)}}\)

\( =  - \frac{{GMm}}{{2R}} - \frac{{GMm}}{{6R}}\)

\( =  - \frac{{4GMm}}{{6R}} =  - \frac{{2GMm}}{{3R}}\)

\(\therefore \) Difference between initial and final energy,

\({E_f} - {E_i} = \frac{{GMm}}{R}\left( { - \frac{2}{3} + \frac{1}{2}} \right) =  - \frac{{GMm}}{{6R}}\)