Question

Scurrilous con artists have been known to represent gold-plated tungsten ingots as pure gold and sell them at prices much below gold value but high above the cost of tungsten. With what accuracy must you be able to measure the mass of such an ingot in and out of water to tell that it is almost pure tungsten rather than pure gold?

a. The accuracy should be within 0.01%.

b. The accuracy should be within 0.10%.

c. The accuracy should be within 1.00%.

d. The accuracy should be within 10.0%.

Answer 1

To determine if an ingot is tungsten or gold, the measurement accuracy must be within 0.01% because of the minimal difference in densities, enabling the detection of the material by calculating its volume and density using Archimedes' principle.

Step-by-step explanation:

To determine with what accuracy you must be able to measure the mass of such an ingot in and out of water to tell that it is almost pure tungsten rather than pure gold, we need to first understand the principle of Archimedes' principle which relates to the buoyancy force experienced by an object submerged in a fluid and the density difference between materials (tungsten and gold in this case).

Pure gold has a density of about 19.3 g/cm3, and tungsten has a density of about 19.25 g/cm3. The difference in densities is therefore very small. To detect this difference, you will need to measure the mass very accurately, both in and out of water. Using Archimedes' principle, when an object is submerged in water, it displaces water equal to its volume and loses weight equal to the mass of that water. The difference in mass will show the volume of the object based on the weight of displaced water, allowing you to calculate the density.

Since we are dealing with very close density values, the accuracy of measurement must be within 0.01% to detect the difference in densities confidently, and hence option 'a' would be correct.