Question

Three particles each of mass m are placed at the corners of an equilateral triangle of side d. Calculate the work done in increasing the sides of triangle from d to 2d.

Answer 1

Given,

Three particles having mass $m$

Sides of the triangle is $d$

So, Gravitational potential energy $=-\frac{G{M}^2}{d}$

Since there are three pairs of a particle in the system.

So,

The potential energy of the system is :

$E_{pi}=3\times -\frac{G{M}^2}{d}=-3\frac{G{M}^2}{d}$

After the length of the triangle is increased to$2d$ the new potential is:

$E_{ef}=3\times -\frac{G{M}^2}{2d}=-3\frac{G{M}^2}{2d}$

Thus, the work done is:

$-3\frac{G{M}^2}{2d}--3\frac{G{M}^2}{d}=-3\frac{G{M}^2}{2d}$