High School

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A solid metal sphere with radius [tex]r_a[/tex] is located at the center of a hollow, metal, spherical shell with radius [tex]r_b[/tex]. If the two objects share the same center, what is the relationship between [tex]r_a[/tex] and [tex]r_b[/tex]?

Answer :

In physics, for a solid sphere center in a hollow spherical shell sharing the same center, ra is the radius of the solid sphere and rb is the radius of the hollow sphere with the relationship ra < rb.

The relationship between ra and rb for a solid metal sphere located at the center of a hollow, metal, spherical shell, where both objects share the same center, is that ra < rb. This means that the radius of the solid sphere (ra) is smaller than the radius of the hollow spherical shell (rb). In the context of physics, particularly when discussing concepts such as gravity, electric fields, or moments of inertia, this relationship between the radii is important.

For instance, according to the shell theorem, the force outside the hollow spherical shell (at any point beyond rb) is as if the entire mass of the shell were concentrated at its center, thus not affecting the solid sphere inside. The same is true for the solid sphere—the mass within any radius r exerts the same force as if all of the mass were concentrated at the center.

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