Find the potential energy of system of 4 particles each of mass 'm' placed at the vertices of square of - Physics - Gravitation

Question

Find the potential energy of system of 4 particles each of mass 'm'
placed at the vertices of square of side 's' also obtain the
potential energy at the centre of the square

Please explain the answer and the method of this
answer

Roop Narayan · Accepted Answer

Dear studentGravitational Potential energy of a system is given byPE=-Gm1m2rpotential at a distance r due to a mass is given by PE=-Gmrr= distance b/w two particlessystem has 4 paricles,Total PE= PE of two particles takenat a time=PE of A,B+PE of A,C+PE of A,D+PE of B,C+PE of B,D+PE of C,D   (repeated groups are taken only once)=-Gm2rAB+-Gm2rAC+-Gm2rAD+-Gm2rBC+-Gm2rBD+-Gm2rCD=-Gm21AB+1AC+1AD+1BC+1BD+1CDfind out the distances using geometryAC=BD=2lAB=BC=CD=CA=lputting in above equation we get PE of system=-Gm21l+1l+1l+1l+12l+12l=-Gm24+2lNote,potentialenergy at entre cannot be found out because their is no massonly potential can be foundthat is what is done in the solution given in the figOA=OB=OC=OD=l2potential at centre==-GmrAO+-GmrBO+-GmrCO+-GmrDO=-Gm2l+2l+2l+2l=-42Gml

Find the potential energy of system of 4 particles each of mass 'm' placed at the vertices of square of side 's' also obtain the potential energy at the centre of the square. Please explain the answer and the method of this answer

Find the potential energy of system of 4 particles each of mass 'm' placed at the vertices of square of side 's' also obtain the potential energy at the centre of the square.

Please explain the answer and the method of this answer