The problem states: invent to a way to measure specific gravity of various liquids in assorted bottles given
1 test tube 1 small vial of mercury 1 pen 1 ruler 1 beaker of water (500 ml)
I know this problem will involve Archimedes' Principle and that specific gravity is the ratio of density of liquid/ density of water. My assumption is that the density of water is known (997 kg/m^3).
My proposed solution is:
step 1: label starting point of water and hold ruler next to beaker step 2: pour mercury into the tube and put the tube into the beaker of water and note the displacement of water with the pen. The volume of water displaced times its density is equal to the mass of water displaced.
I am not sure where to go from here..... I could dump out the mercury and pour the liquids into the test tube one at a time to measure the change in height of water. But I wouldn't be able to know the volume of the liquids...