Question

Three particles of mass 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 2a.

Answer 1

The work done in increasing the side of the triangle from a to 2a is equal to the difference of the potential energies of the system.
i.e., work done = final potential energy of the system $-$ initial potential energy of the system

$$\begin{gathered} \therefore W=-3\frac{G{m}^2}{2a}-\left(-3\frac{G{m}^2}{a}\right) \\ \Rightarrow W=3\frac{G{m}^2}{2a} \end{gathered}$$