How Does Radial Density Variation Affect Gravity on a Sphere's Surface?

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The discussion revolves around calculating the acceleration of gravity at the surface of two spheres with different density distributions. Sphere S1 has a constant density, while sphere S2's density varies with radial distance as p(r) = C/r. The key equation for gravitational acceleration is g = GM/R, where M is mass and R is radius. Participants express uncertainty about the relationship between acceleration and the given parameters, questioning whether the acceleration of gravity would be the same for both spheres despite their equal masses. The conversation highlights the need for clarification on how radial density variation impacts gravitational acceleration.
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Homework Statement



1. Two spheres S1 and S2, have equal radii R, and equal masses M. The density of sphere S1 is constant, whereas that of sphere S2 depends on the radial distance according to p(r)= C/r. If the acceleration of gravity at the surface of sphere is g1, what is the acceleration of gravity at the surface of sphere S2 ?



Homework Equations



g=GM/R


The Attempt at a Solution



1. SO I cannot recall any relationship between acceleration and all the givens. Can you guys give me a hint on what equation, formula should I use ? What should I find first ?
 
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Maybe the problem is more complicated than this, but...
Isn't the acceleration of gravity the same for both spheres, since they have equal masses?
 
I am not sure. Anyone ? What do formula should I use here ?
 
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