Archimede was given another task by the king again. The king had asked a goldsmi

Question

Archimede was given another task by the king again. The king had asked a goldsmith to make a gold ring for his queen. Again, the king was suspicious of the goldsmith's honesty, so he decided to let Archimede find out whether the ring was made of pure gold. Archimede weighted the ring and found a reading of 0.1582 N on the scale. Using a string, he suspended the ring from the scale and, with the ring submerged in water, weighted it again to find a new reading of 0.15 N. The density of water is 1000 kg/m3 and that of gold is 19300 kg/m3. What was the magnitude of the buoyant force acting on the ring? What was the density of the ring? Was it made of pure gold?

Explanation / Answer

a)

buoyant force = FB

FB = 0.1582 - 0.15 = 0.0082 N

b)

FB = (rho_water) g V

==> V = FB/((rho_water) g)

==> V = 0.0082/(1000*9.8)

==> V = 8.3673 x 10^-7 m3

masss of the ring = m = 0.1582/9.8 = 0.016143 Kg

rho = m/V = 0.016143/8.3673e-7 = 19293 = 19300 Kg/m3

Yes, it is made of pure gold

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