Gravitational Field due to a sphere can be analyzed in two
cases of Hollow and a Solid Sphere. For a hollow sphere by symmetry we can
analyze that net gravitational field strength at interior points is equal to
zero and it can also be analyzed by considering two diametrically opposite
elements on the surface of shell. For outer points of the shell by spherical
symmetry it is similar to that of a point mass. See the below video for
understanding of the same:
Gravitational Field due to a solid sphere can be analyzed by
its spherical symmetry for outer points like a spherical shell and for interior
points we can consider a point inside of the sphere and divide the sphere in
two parts, one inner sphere of radius up to the point and one outer shell of
inner radius up to the point and outer radius equal to that of the sphere. See
the video below for the analysis:
Gravitational Field due to a Cylinder at points in its outer
surrounding the field direction will be radial and similar to that of a long
linear mass distribution. For this analysis we find the gravitational field strength
due to a long thread of uniform linear mass density. At outer points of
cylinder the field will remain the same. See the video below for the analysis:
