Question

A king's crown is said to be solid gold but may be made of lead and covered with gold. when it is weighed in air, the scale reads 0.475 kg. when it is submerged in water the scale reads 0.437 kg.is it solid gold? if not, what percent is mass is gold? (density of gold= 19.3x10^3 kg/m^3)

Answer 1

m=0.475 kg, m1 =0.437 kg,
density of lead = 11.4 * 10^3 kg/m^3
m1•g = m•g – F(buoyancy) =>
m1•g = m•g – ρ(w)•V•g,
V= (m - m1)/ρ(w) = (0.475-0.437)/1000 =3.8•10^-5 m^3.

m1•g = ρ(x) •V•g – ρ(w)•V•g ,
m•g = ρ(x) •V•g,
ρ(x) = m/V = 0.475/3.8•10^-5 =12.5•10^3 kg/m^3
(b)
19.3•10^3•x +11.4•10^3•(100-x) = 12.5•10^3•100,
19.3•x+11.4•(100-x) = 12.5•100,
7.9•x = 110,
x =13.92% ≈14%.
The crown is roughly 14% gold and 86% lead.