Question

Vadim bought his wife a "gold" bracelet from a guy on the street for $100. If he drops it in a beaker of water and the volume raises 400 cm3 and the mass is determined to be 0.5 kg, then is the jewelry gold? If it is not gold then what do you think it is made of?

Answer 1

Answer: It is not gold. The density is 1.25 g/cm3, very little compared with gold.

Explanation:

According to Archimedes’ principle, any body submerged in a liquid, receives an upward force, called buoyant force, which magnitude is equal to the weight of the liquid that displaces.

This weight can be calcultated as follows:

Fb= δH2O . Vbody g

We are told that the volume of the liquid displaced (equal to the volume of the body as it is completely submerged in water) is 400 cm3.

If we know that the mass of the bracelet is 0.5 Kg, we can find out the density of the material, just applying the same relationship between mass, density and volume:

m = δbracelet. V  

δbracelet = m / V = 500 g / 400 cm3= 1.25 g/cm3

As the gold density is approximately 19.3 g/cm3, it is clear that the bracelet is not made from gold, but from something less dense.