The story goes that the king of Syracuse suspected a goldsmith of having substit
ID: 1458810 • Letter: T
Question
The story goes that the king of Syracuse suspected a goldsmith of having substituted some of the gold with silver in a crown he was commissioned to make. He wanted Archimedes to find out if the crown was made purely of gold without damaging the crown. Archimedes is said to have discovered his principle while solving this problem.
Suppose the crown weighs 8.82 N in air and 8.25 N when it is submerged fully in water.
(a) What is the mass of the crown?
(b) What is the volume of the crown?
(c) How can you conclude that the crown is not made of pure gold?
(d) If the crown is made only of gold and silver, what percentage of the total mass is due to silver?
(e) What percentage of the total volume is due to silver?
Explanation / Answer
(a)
Weight of Crown in Air = 8.82 N
Weight = m*g
m = 8.82/ 9.8
m = 0.9 Kg
Mass of Crown , m = 0.9 Kg
(b)
Let Volume of Crown = v
Fb = 8.82 - 8.25
Fb = 0.57 N
Density of Water * volume of water displaced = 0.57/9.8
1000 kg/m^3 * volume of object = 0.57/9.8
Volume of crown = 5.82 * 10^-5 m^3
Volume of crown = 58.2 cm^3
(c)
Density = Mass/ Volume
Denisty = (0.9 * 10^5) / 5.82
Denisty = 15463.92 kg/m^3
Denisty = 15.46 g/cm^3
As the density of Crown does not match density of pure gold(19.32 g/cm^3), therefore we can say it is not made of pure gold.
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