Question:
Three particles of mass $\mathrm{m}$ each are placed at the three corners of an equilateral triangle of side a. Find the work which should be done on this system to increase the sides of the triangle to $2 a$.
Solution:
Work done $=\Delta U=$ final P.E - initial P.E $=U_{f}-U_{i}$
$=3\left(\frac{-G m m}{2 a}\right)-3\left(\frac{-G m m}{a}\right)$
$=\left(\frac{3 G m^{2}}{2 a}\right)$