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 possible pairs of masses. For three masses $m_1,m_2,m_3$ at distances $r_{12},r_{13},r_{23}$ respectively, the total potential energy is given by:$$U=-G\left(\frac{m_1{m}_2}{r_{12}}+\frac{m_1{m}_3}{r_{13}}+\frac{m_2{m}_3}{r_{23}}\right)$$ In this case,$m_1=m_2=m_3=m$ and $r_{12}=r_{13}=r_{23}=a$. There are 3 such pairs.$$U=-G\left(\frac{m\cdot m}{a}+\frac{m\cdot m}{a}+\frac{m\cdot m}{a}\right)=-\frac{3G{m}^2}{a}$$