Question

Find the potential energy of a system of four paticlea each of massm placed at the vertices of a square of side. Also obtain the potential at the centre of square

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#