Question

what is the force of attraction between hollow

spherical shell of uniform density on a point

mass inside ?

Answer 1

Consider a point A inside a spherical shell, at some distance apart from center. If there is a gravitational field acting on this point, it must be along radial direction, due to symmetry in angular direction.

Now, consider two solid angles in opposite directions along the radius subtended from the point A. The mass that is enclosed in these solid angles is directly proportional to the square of distance from the point A to the point on the shell (m = density * surface area * thickness) and the gravitational field is inversely proportional to the square of distance. hence the gravitational field due to these two opposite masses cancel each other. Resulting in zero gravitational field.