EK Physics fluids question

[AZFutureDoc]

Hey I have a quick question on question 100, on age 81 of the manual.

A helium balloon will continue to rise until:


A: temperature inside balloon is equal to temperature outside balloon
B: Mass of helium in balloon is equal to mass of air outside balloon
C: Weight of balloon is equal to upward air current
D: Density of air in balloon is equal to density of air outside balloon

Now, you throw out A and C immediately, but I got down to B and D. My reasoning, after setting the buoyant force equal to the gravitational force, was that

(density of air)(g)(volume of balloon)=mg
(density of air)(volume of balloon)=m
(m air)=(m balloon)

I got this far, and chose B, not really paying attention to the fact the the wording of the question doesn't specify all the air on the planet, or just air displaced.

Now EK, takes exactly what I did one step further, and says

(density of air)(volume of balloon)=(density of balloon)(volume of balloon)

(density air)=(density balloon), or
(density air)=(density helium)

So since density and volume give mass, why is mass so incorrect? Is it because the question probably means all the air on earth, not jus displaced? This is seriously my only weakness, this density, Archimedes, S.G. stuff!

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[sleepy425]

Hey I have a quick question on question 100, on age 81 of the manual.

A helium balloon will continue to rise until:


A: temperature inside balloon is equal to temperature outside balloon
B: Mass of helium in balloon is equal to mass of air outside balloon
C: Weight of balloon is equal to upward air current
D: Density of air in balloon is equal to density of air outside balloon

Now, you throw out A and C immediately, but I got down to B and D. My reasoning, after setting the buoyant force equal to the gravitational force, was that

(density of air)(g)(volume of balloon)=mg
(density of air)(volume of balloon)=m
(m air)=(m balloon)

I got this far, and chose B, not really paying attention to the fact the the wording of the question doesn't specify all the air on the planet, or just air displaced.

Now EK, takes exactly what I did one step further, and says

(density of air)(volume of balloon)=(density of balloon)(volume of balloon)

(density air)=(density balloon), or
(density air)=(density helium)

So since density and volume give mass, why is mass so incorrect? Is it because the question probably means all the air on earth, not jus displaced? This is seriously my only weakness, this density, Archimedes, S.G. stuff!

The thing is, when it says, the mass of the air inside is equal to the mass of air outside the balloon, it's a meaningless statement. I mean, it can't mean the mass displaced because that's how it would be said, so it would have to be the mass of all air not in that balloon, which means all air everywhere in the universe. D is correct, because when density of air inside equals density of air outside, that means that the mass of air displaced by the balloon equals the mass of the air inside the balloon (because if the balloon displaces a certain volume V, and the density inside and outside the balloon is the same value, call it D, then the mass inside and the mass displaced are both V*D.)