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

The potential energy of the system = sum of potential energies of all the three possible distinct pairs .
i.e., `U = U_(AB) + U_(AB) +U_(CA)`
` = (-G(m)(2m))/a +(-G(2m)(3m))/a + (-G(3m)(m))/a `
` = (-11Gm^(2))/a `
when the side a is changed to 2a , the potential energy U . = `(-11Gm^(2))/(2a)`
(ii) The work done on the system = `U.-U`
` =(11Gm^(2))/(2a)`
Note :
The work done by the system = The work done by the gravitational force
` = -(U.-U)`
` = (-11Gm^(2))/(2a)`
The work done on the system = The work done against the gravitational force
= The work done by the external force
` = U. - U `
` = (11Gm^(2))/(2a)`