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 56.6 N when it is completely submerged in water. Take the density of gold to be 19300 kg/m3, the density of lead to be 11340 kg/m3, and the density of water to be 1000 kg/m3. Also, use g = 9.8 m/s2. The average density of the crown is 17600 kg/m3.
a. What percentage (by weight) of this crown is made of gold? The rest, we assume, is lead.