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

$\rho_{\mathrm{F}}=0.815 \mathrm{g} \mathrm{L}^{-1}$

Physics 101 Mechanics

Chapter 11

Fluid Statics

Fluid Mechanics

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So here are comedians. Principle applies. We're here. We can say that the fraction submerged, which we're just gonna call f, would be equaling the average density of the object divided by the density of the fluid with with the object is placed in. And so the density of the fluid would simply be equal to the average density of the object divided by half the fraction submerged. This would be equal 2.750 grams per mil. Leader divided by 0.92 That's amazing. So here are comedians. Principle applies. We're here. We can say that this is gonna be the density of the fluid. Is that equaling 0.815 grams per mil leader? We know that this is equaling 0.815 grams per cubic centimeter. Given that one middle leader is equaling one cubic centimeter and then converting, we can say that this is gonna be equaling. Ah, 1000 whether we can say one kilogram for every 1000 grams and then a fraction submerged, which we're just gonna call F would be equaling the average density of the object divided by the density of the fluid with with the object is placed in and so the density of the fluid would simply be equal to the average density of the object divided by half the fraction submerged. This would be equal 2.750 grams per mil leader divided by 0.92 There are 100 centimeters for every one meter quantity cubed. And so we can then say that the density of the fluid is going to be equal to 815 kilograms per cubic meter. This would be our final density for the fluid. That is the end of the solution. This is gonna be the density of the fluid. Is that equaling 0.815 grams per mil leader? We know that this is equaling point 815 grams per cubic centimeter. Given that one middle leader is equaling one cubic centimeter and then converting, we can say that this is gonna be equaling Ah, 1000 whether we can say one kilogram for every 1000 grams and then thank you for what? There are 100 centimeters for every one meter quantity cubed. And so we can then say that the density of the fluid is going to be equal to 815 kilograms per cubic meter. This would be our final density for the fluid. That is the end of the solution. Thank you for watching Jane.

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