What is the relation between a shell and a solid sphere?

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athrun200
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Homework Statement




Printed textbook problem 21 on a spherical shell of mass m' and radius r', giving the gravitational potential inside and outside the shell, then results for a solid sphere: force and potential inside and outside the earth, with a hint about the surface force mg.

Homework Equations





The Attempt at a Solution



What is the relation between a shell and a solid sphere?
Can you give me some hints?
 
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  • Printed textbook problem 21 on gravitational potential of a uniform spherical shell, with piecewise potential formulas and the solid sphere results F = -mgR^2/r^2 e_r, phi = -mgR^2/r, F = -mgr/R e_r, and phi = (mg/2R)(r^2 - 3R^2).
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A solid sphere can be thought of as composed of an arbitrarily large number of smaller shells...
How could you 'add up' the effects of many smaller shells, to construct a sphere?