Question

When there are 2 point masses M and m such that Many is fixed . m is brought from infinity to a point A then it it derived that for the system of two masses , gravitational potential (GP ) at point A = -GM/R. It means for mass m , GP is found with respect to mass M

Then why for a ring , while calculating GP (when dm is assumed as the mass of the element ) GP at point Of outside the ring at a distance of r from centre and z distance from the element= -Gdm/z.
Why it's not -GM/z .

As when there are two masses the GP at the point A was with respect to the another body of mass M !!

Answer 1

''When there are 2 point masses M and m such that Many is fixed . m is brought from infinity to a point A then it it derived that for the system of two masses , gravitational potential (GP ) at point A = -GM/R. It means for mass m , GP is found with respect to mass M.'' here both mass M and m are concentrated at a point. so we take whole mass m and M for derivation. But for " while calculating GP (when dm is assumed as the mass of the element ) GP at point Of outside the ring at a distance of r from centre and z distance from the element= -Gdm/z. " we take small mass element dm for derivation, because ring 's mass is not concentrated at a point . it's spread around a circle . so we take dm as a small mass element which is concentrated at that particular point then integrate whole equation to find total gravitational potential (GP ) for the ring.