Find the work done in bringing three particles, each having a mass of 0.1 kg from large distance to the vertices of an equilateral triangle of 10 cm in a gravity free region. Assume that no change of kinetic energy is involved in the bringing particles.

We note here that all three particles have same mass. Hence, product of mass in the expression of gravitational potential energy reduces to square of mass.

The gravitational potential energy of three particles at the vertices of the equilateral triangle is:

U = -^{3 G m2}/_a

where "a" is the side of the equilateral triangle.

Putting values we get, U = ^{3 × 6.67 × 10-10 × (0.1)2}/_0.1

∴ U = -2 × 10^-11 J

Hence, work done by external force in bringing the three particles from large distance is

∴ W = U = -2 × 10^-11 J