Question

You are present with a baker of fluid that you think is olive oil(which can have a specific gravity of 0.91-0.92 depending upon the "grade" of oil). You are also given a block of paraffin wax that is 2mm x 5mm x 10mm in shape, that has a specific gravity of 0.82-0.96. report all the calculation results to 3 significant digit accuracy.

a) First you place the block of paraffin into a baker of distilled water(SG=1) , with the 2mm side perpendicular to the surface of water- greatest surface area parallel to water's surface, and note that only 0,3 mm remains above the surface of the water. what is the actual specific gravity of your sample based on this measurement?

b) You now place the paraffin block in the oil, again with the 2mm side perpendicular to the fluid's surface. the block sinks into the oil with only 0.15 mm above the surface of the water. What is the specific gravity of your oil sample , and it is , indeed, olive oil?

c)if the paraffin block were to sink until it's top surface were just at the level into which you submerged it ;... it was totally submerged , but not bellow the surface of fluid, what can you say about the relationship between the paraffin block and the fluid?

Answer 1

The specific gravity of a sample is the ratio of density of the sample to the density of water.

According to Archimedes principle, the ratio of densities is given by

a) Here,

The height of paraffin = 2 mm

Height inside water = 2-0.3 = 1.7 mm

So,

specific gravity of paraffin sample = 1.7/2 = 0.85

b) Now, for the oil, the relative density between oil and paraffin is given by

height inside the liquid = 2-0.15 = 1.85 mm

c) When an object is totally submerged in a liquid, but does not sink, this means that the liquid and the solid has the same density and specific gravity.