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

Consider four masses each of mass m at the corners of a square of side l: See Fig. ,9. We have four mass paris at distance l and two diagonal pairs at distance `sqrt(2)l`
Hence,
`W®=-4(Gm^(2))/(l)-2(Gm^(2))/(sqrt(2)l)`

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