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**Unformatted text preview: **All points on the small hoop indicated in Figure 14.2 have the same distance to the particle m. The magnitude of the gravitational attraction between any of these points and the mass m is therefore the same. The net force between the hoop and mass m acts along the axis connecting the center of the shell and mass m. The area of the hoop is given by Figure 14.2. Shell theorem. and its mass m is equal to The net force is equal to The angles [theta] and a can be eliminated by using the following relations: and Differentiating the first of these two equations with respect to [theta] we obtain or Further more we see that The total force acting on mass m can now be obtained easily The shell theorem immediately shows that a sphere of uniform density (and mass M) attracts an external particle as if all the mass of the sphere is concentrated in its center. In a similar fashion we can proof that a uniform shell of matter exerts no gravitational force on a particle located inside it ....

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