A sphere shell has inner radius R, outer radius R, and mass M, distributed uniformly throughout the shell. Find the magnitude of the gravitational force exerted on the shell by a point particle of mass m located at a distance d from the center, outside the inner radius and inside the outer radius.

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Mass of the sphere =

Point P is at a distance of d from the center and there is a particle of mass m located there.

The mass of the spherical shell that will cause force will be mass located between the spheres of radius d and radius R_{1}.

That is mass of volume

Mass is distributed uniformly in the shell. Thus density of the shell is

Thus

Thus force exerted on m is =

or