Find the gravitational potential energy of a system of four particles, each of mass `m` placed at the verticles of a square of side `l`. Also obtain the gravitaitonal potential at centre of the square.

Explanation

The system has four pairs with distance `l` and two diagonals pairs with distance `sqrt(2)l`.
`U=-4(Gm^(2))/l-2(Gm^(2))/(sqrt(2)l)=-(2Gm^(2))/l(2+1/(sqrt(2)))`
the gravitational potential at the centre of the square is
`V=` Algebraic sum of potential due to each particle
`V=-(4Gm)/r=-(4sqrt(2)Gm)/l ( :' r=(sqrt(2)l)/(2))`