What is the gravitational potential at the centre of a uniform solid sphere of mass 'M' and radius 'R' ( if potential due to the sphere at the infinity is GM/R)

 

 

Dear student

Following is the detailed account of how to derive gravitational potential at the center of the solid sphere.

 

The uniform solid sphere of radius “a” and mass “M” can be considered to be composed of infinite numbers of thin spherical shells. We consider one such thin spherical shell of infinitesimally small thickness “dx” as shown in the figure.

Case:  The point lies inside the sphere
We calculate potential in two parts. For this we consider a concentric smaller sphere of radius “r” such that point “P” lies on the surface of sphere. Now, the potential due to whole sphere is split between two parts :

 

 

 

We hope that resolves your query.

 

Regards

 

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