Three particles each of mass m are placed at the corners of an equilateral triangle of side d. Calculate
(a) the potential energy of the system, (b) work done on this system if the side of the triangle is changed from dto 2d.

Explanation

(a)As in case of two-particle system potential energy is given by `((-"Gm"_(1)m_(2))/(r)),` so
`U_(A)=U_(12)+U_(23)+U_(31)`
So, `U_(A)=-3("Gmm")/(d)=-(3"Gm"^(2))/(d)`

(b) when d is changed to 2d, `U_(B)=-(3"Gm"^(2))/(2d)`
So, work done = `U_(B)-U_(A)=(3"Gm"^(2))/(2d)`