Question 3 1 pts Jane wants to get her fiance a custom engagement ring, and she decides to buy the diamond separately and then commission an artist to make a bespoke ring to match. She goes online and finds a lesser-known website that sells diamonds at significantly lower prices than their competitors. This makes Jane really happy because it means she's able to buy a beautiful diamond that's much larger than she expected to be able to buy, but she also feels a bit uneasy as the diamond is really expensive, and she's not sure if the website is reputable. When she shows the diamond to her friend Jack, who is a jeweler, he notes that the way it scatters light doesn't seem to be quite the same as a diamond. He suggests that it could instead be made of cubic zirconia, a synthetic material often used to imitate diamond. Jane panics, and she asks Jack if there is a way to make sure her diamond is real. "Sure" he says, and he gives her the following directions: 1. Weigh the stone on a scale on your countertop. 2. Put the scale under water and weigh the stone under water. Use the results of these weight measurements to compute the density of the stone, and compare it to the density of diamond. Compare the density you determine in this way to the densities of diamond and cubic zirconia, and it should be obvious whether or not it's a real diamond. Jane does this process and gets a scale reading of 0.47 g in step 1, and a scale reading of 0.39 g in step 2. Use these weight readings to compute the density of the stone and put this density value (in grams per cubic centimeter) in the answer box. Decide whether it's likely diamond or cubic zirconia. The density of diamond is about 3.5 g/cma, and the density of cubic zirconia is about 5.8g/cm?. Hints: Draw separate free body diagrams for when the stone is on the scale on the countertop and when the stone is on the scale under water, and apply Newton's Second Law. Use Archimedes' Principle. Note that even though the scale readings are given in grams, which is a mass unit, scales actually measure a force, not a mass. In fact, scales measure the contact force (normal force) between the object on the scale and the surface of the scale. To get the force reading from the mass reading, multiply the scale's mass reading by g = 9.8 m/s3