Finding the Ratio of r/R for a Submerged Hollow Sphere

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Homework Help Overview

The problem involves a hollow sphere with inner radius r, outer radius R, and density p, which is floating in a fluid with density pf. The specific scenario is that half of the sphere is submerged, and the task is to find the ratio of r to R when the ratio of densities p to pf is given as 3.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of Archimedes' Principle and the relationship between the mass of the sphere and the buoyant force. There is confusion regarding the symbols used for volume in the equations presented, and participants are questioning the consistency of these symbols.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the equations and their derivations. Some guidance has been offered regarding the need to properly define symbols and relationships, but no consensus or resolution has been reached yet.

Contextual Notes

There is a focus on ensuring that the equations used are consistent and correctly represent the physical situation. Participants are also navigating the implications of the given density ratio and how it affects the calculations.

momu
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An empty hollow sphere of inner radius r, outer radius R and density p floats so that exactly one half is submerged in a fluid of density pf.
a.) if p/pf is =3 what is the ration of r/R.

ok well
mg=pVg
m=pV/2

V=4/3pi(R^3-r^3)

m=p(4/3pi(R^3-r^3)

I don't know where to go from here any help is appreciated thanks.
 
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momu said:
mg=pVg
m=pV/2

Are you talking about the same V in the two eqns? First decide upon the symbols properly.

Then directly apply Archimedes' Principle.
 
no its the same equation just canceled out the g. but you Its the same V
 
So, the 2nd eqn follows from the 1st? This is a matter of elementary algebra! Think again and write eqns properly.
 
F=0
mg-fB=0
m=p * Vs (volume of sphere)/2

Know for the volume i have 4/3pi(R^3-r^3)
 
First clear the matter of the two eqns in post #2. What do the two different V's represent? And how can eqn 2 follow from eqn 1?
 

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