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

[momu]

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.

 

[Shooting Star]

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.

 

[momu]

no its the same equation just canceled out the g. but you Its the same V

 

[Shooting Star]

So, the 2nd eqn follows from the 1st? This is a matter of elementary algebra! Think again and write eqns properly.

 

[momu]

F=0
mg-fB=0
m=p * Vs (volume of sphere)/2

Know for the volume i have 4/3pi(R^3-r^3)

 

[Shooting Star]

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?