You, Archimedes, suspect that the king\'s crown is not solid gold but is instead

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 55.7 N when it is completely submerged in water. Take the density of gold to be 19,300 kg/m3, the density of lead to be 11,340 kg/m3, and the density of water to be 1000 kg/m3. Also, use g = 9.8 m/s2.

(a) What is the average density of the crown?

(b) What percentage (by weight) of this crown is made of gold? The rest, we assume, is lead.

Explanation / Answer

here,

Archimedean thrust , F = Wa-Ww

F = 60 - 55.7

F = 4.3 N

Volume V = 4.3/9.8 = 0.439 dm^3

p c = Wa/V = 60/0.439 = 136.74 N/dm^3

called x the gold amount in p.u.

136.74 = (19.3*9.8*x + 11.34*9.8(1-x))

x = 0.328

so, the amount of gold is 32.8 %

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