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

(a) As in case of two-particle system potential energy is given by `(-Gm_(1)m_(2)//r)`, so
`U = U_(12) + U_(23) + U_(32)`
or `U_(i) = -3(Gm m)/(d) = -(3Gm^(2))/(d)`
(b) When d is changed to 2d,
`U_(f) = - (3Gm^(2))/(2d)`
Thus work done in changing in potential energy is given as
`W = U_(f) - U_(i) = (3Gm^(2))/(2d)`