Question

Find the potential energy of a system of four particles.each of mass "m" place at the vertices of a square of side " l " also obtained the potential at the centre of the squqre?

Answer 1

For a mass of `m` potential energy of a test mass at distance r is given as `(G*m/r)`

Total potential energy of the system is `(Gm^2)/l ×4+ 2*(Gm^2)/(sqrt(2)l)` or,`4 (Gm^2)/l+sqrt(2)(Gm^2)/l` ( Due to `4` mass at the vertices and 2 diagonally present,length of diagonal is `sqrt(2)l`)

Distance of each mass from the centre is =length of diagonal/2 i.e `l/sqrt(2)`

So,potential energy at the centre for 4 such mass is `((Gm)/(l/(sqrt(2)))*4)` i.e `4sqrt(2)(Gm)/l`