Question

Find the density of a fluid in which a hydrometer having a density of 0.750 g/mL floats with 92.0% of its volume submerged.

$0.815 \textrm{ g/mL}$

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This is College Physics Answers with Shaun Dychko. A hydrometer with density 0.750 grams per milliliter is floating in a fluid of unknown density and we know the fraction of the hydrometer that is submerged is 92.0 percent so we are going to find the density of the fluid given this information. So the fraction submerged is the density of the thing floating divided by the density of the fluid. So we multiply both sides by

*ρ F*divided by fraction submerged and we'll solve for the density of the fluid. So density of fluid is the density of the hydrometer divided by the fraction submerged. So that's 0.750 grams per milliliter divided by 92 percent written as a decimal, multiplying by 1 for every 100 percent, and this gives us 0.815 grams per milliliter is the density of the fluid.