Question

You, Archimedes, suspect that the king’s crown is not solid gold but is instead gold-plated lead. To test your theory, you weigh the crown, and find it to weigh 60.0 N, and to have an apparent weight of 56.5 N when it is completely submerged in water. Take the density of gold to be 19300 kg/m, the density of lead to be 11340 kg/m, and the density of water to be 1000 kg/m. Also, use g = 9.80 m/s.
(a) What is the average density of the crown?
_______ kg/m (b) What percentage (by weight) of this crown is made of gold? The rest, by the way, is lead.

Answer 1

The apparent weight is the difference between the weight and the buoyant force:

According to Archimede's principle, the buoyant force is equal to the weight of the displaced fluid (water in this case):

Now that we know the volume of the crown we can calculate it's avg density:

The purity can be obtained from:

This means that only 72.9% of the crown is made of gold