Question

The density of gold is 19.32 kg/l. A gold colored piece of metal was massed out to be about 5,230 mg. The volume of the metal measured by placing it in 14.6 cL of water and the water level rose to 17.2 cL. Is this piece of metal gold

Answer 1

Answer on Question #71906, Physics / Other

Question. The density of gold is $19.32 \, kg/L$. A gold colored piece of metal was massed out to be about $5,230 \, mg$. The volume of the metal measured by placing it in $14.6 \, cL$ of water and the water level rose to $17.2 \, cL$. Is this piece of metal gold?

Given.

$$\rho_0 = 19.32 \, kg/L;$$ $$m = 5,230 \, mg = 5,230 \cdot 10^{-3} \, g = 5,230 \cdot 10^{-6} \, kg;$$ $$V_1 = 14.6 \, cL = 14.6 \cdot 10^{-2} \, L;$$ $$V_2 = 17.2 \, cL = 17.2 \cdot 10^{-2} \, L.$$

Find.

$$\rho - ?.$$

Solution.

The volume of the metal is

$$\Delta V = V_2 - V_1 = 17.2 \cdot 10^{-2} - 14.6 \cdot 10^{-2} = 2.6 \cdot 10^{-2} \, L$$

Hence

$$\rho = \frac{m}{\Delta V} = \frac{5,230 \cdot 10^{-6}}{2.6 \cdot 10^{-2}} = 2011 \cdot 10^{-4} \, kg/L = 0.2011 \, kg/L$$ $$\rho \neq \rho_0$$

Answer. it's not gold

Answer provided by https://www.AssignmentExpert.com