A sphere with uniform mass distribution is a symmetrical body. Due to this symmetry, the gravitational field in its surrounding can be considered in radially inward direction just like a point mass. We can discuss the Gravitational Potential due to uniform hollow and solid spheres.
Gravitational Potential due to a Hollow Sphere
In surrounding region of a uniform hollow sphere, the gravitational potential can be considered like a point mass, and same expression of potential due to a point mass is valid for the gravitational potential outside a uniform hollow sphere. This includes the points on its surface (for all x greater than or equal to its radius R).
As we know that, at interior points the gravitational field is zero, no work is required in displacement of a point mass inside the hollow sphere. Hence, gravitational potential must be same everywhere inside the sphere which will be equal to that of the surface. For analysis and discussion on gravitational potential due to a uniform hollow sphere watch the video belowhttps://youtu.be/dCuUhJLl_LU
Gravitational
Potential due to a Solid Sphere :
Similar to the above case, gravitational potential in the outside region of a solid sphere can also be given by
the expression of potential due to a point mass because of symmetry including
the outer surface points of the sphere.
At interior points as gravitational field is non-zero, we
need to calculate the potential of the sphere by calculating
the potential difference between surface points and any interior point. The
analysis and discussion on gravitational potential due to a solid sphere is
analyzed in the video given below –