Find the potential energy of a system of four particles placed at the vertices of a square of side l. Also obtain the potential at the centre of the square.

Explanation

Consider four masses each of mass m at the corners of a square of side l. see fig, we have four mass pairs at distance l and two diagonal pairs at distance `sqrt2l`

Hence , `U(r)=-4(Gm^2)/1-2(Gm^2)/(sqrt2l)`
`=-(2Gm^2)/l (2+1/sqrt2)=-5.41 (Gm^2)/l`
The gravitational potential at the centre of the square `(r=sqrt2l//2)` is
`V(r)=-4sqrt2(Gm)/l`