Physics - Gravitation Question with Solution | TestHub

The gravitational potential energy of a system of point masses is the sum of the potential energies of all unique pairs of masses. For three masses at the vertices of an equilateral triangle, there are three pairs, each separated by distance $L$. The potential energy for each pair is $U_{pair}=-\frac{GM\cdot M}{L}=-\frac{G{M}^2}{L}$. Since there are three such pairs, the total gravitational potential energy of the system is $U_{total}=3\times (-\frac{G{M}^2}{L})=-\frac{3G{M}^2}{L}$.