fluids buoyant force ap physics 2 question!!! help

Question

2) The students were discussing future lab work after completing a lab to determine the density of an irregularly shaped object using spring elongation. Student A said they could try submerging the object into glycerin which has a density of about 1250 kg/m^3. Student B said that because the density of glycerin is 5/4 of water's density, then they should get a density for the object that is 5/4 of the actual density. Student A disagreed and said that because the density of glycerin is greater, then there would be more buoyant force so therefore their calculation for the density of the object should be less, probably about 4/5 of the actual density. Which student do you agree with (one, both, neither)? Explain why.

Answer 1

Although it's not clear, I assume that you are comparing the weight of the object by itself (F) and while submerged in a liquid. (F').

The buoyant force is F- F' = ρ_LgV_O and since F = ρ_OgV_O , ρ_O = (F/(F=F') * ρ_L

This means that the density of the solid can be calculated from 2 weights (or stretches) with and without liquid or from two submerged cases with different liquids. Therefore, glycerine works as well as water and will yield the same solid density.

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