Answer to Question #163000 in Mechanics | Relativity for Sage Topaz

Question

A 50 g bracelet is suspected of being gold plated lead instead of pure gold, when it is dropped into a full glass of water, 4.0 cm³ of water overflows. Is the bracelet pure gold? If not, what is the percentage of gold in it? Density of gold is 19 g/cm³  density of lead is 11 g/cm³  

Answer 1

(a) The volume of water displaced equals the volume of the bracelet. Then, we can find the density of the bracelet:

$$\rho=\dfrac{m}{V}=\dfrac{50\ g}{4.0\ cm^3}=12.5\ \dfrac{g}{cm^3}.$$

The density of gold equals $19\ \dfrac{g}{cm^3}$, therefore, the bracelet isn't made of pure gold.

(b) Let the fraction of gold be $x$. Then, we can write the following equation:

$$19x+11(1-x)=12.5,$$ $$8x=1.5,$$ $$x=\dfrac{1.5}{8}\times100\%=18.75\%.$$