Three particle each of mass m are placed at the corners of an equilateral at the corners of an equilateral triangle of side d as shown in figure. Calculate (a) the potential energy of the system, (b) work done on this system if the side of the traingle is changed from d to 2d.

Explanation

(i) The potential energy of the system = Sum of the potential energies of all the three possible distinct pairs

i.e.,`U=U_(AB)+U_(BC)+U_(CA)`
`=(-G(m)(2m))/(a)+(-G(2m)(4m))/(a)+(-G(4m)(m))/(a)`
`=(-14Gm^(2))/(a)`
when the side a is changed to 2a, the potential energy
`U'=(-14Gm^(2))/(2a)`
(ii) The work done on the system = The work done against the gravitational force = The work done by the external force
`=U'-U=(14Gm^(2))/(2a)`.