Conceptual question regarding buoyant force

[coconut62]

A penguin floats first in a fluid of density p0, then in a fluid of density 0.95p0, and then in a fluid of density 1.1p0. a) Rank the densities according to the magnitude of the buoyant force on the penguin, greatest first. b) Rank the densities according to the amount of fluid displaced by the penguin, greatest first.

Answer:
a) All tie. The gravitational force on the penguin is the same.
b) 0.95p0, p0, 1.1p0.

Why? Since the penguin displaces different amounts of water in the three fluids(as part b suggests) surely the buoyant force must be different? (Buoyant force = weight of fluid displaced) For example when the penguin is in fluid of density 0.95p0 half of the body is in the liquid, and when it is in the fluid of density 1.1p0 only a quarter of the body is in the liquid, how can the buoyant forces tie?

Thanks.

 

[Bystander]

a) Rank the densities according to the magnitude of the buoyant force

Answer:
a) All tie. The gravitational force

Keep track of which forces you're playing with, and you'll be fine.

 

[Dale]

how can the buoyant forces tie?

Consider Newtons second law. What would happen if the buoyant force were not equal to the weight?

 

[A.T.]

Since the penguin displaces different amounts of water...

What does "amount" mean here? What measure of amount of displaced fluid is relevant for the buoyant force

 

[Bystander]

Volume. Volume x density x gravity = F

 

[A.T.]

Volume. Volume x density x gravity = F

No it's not just volume, is it?

 

[Bystander]

Yes.

 

[coconut62]

I think I got it:

For all three fluids, weight of fluid displaced is the same, but

Weight = mg = (rho)(V)g

Therefore rho is inversely proportional to V.

For the fluid of highest density, volume displaced is the least, because just a small volume of this fluid already weights the same as a larger volume of another liquid with a lower density.