Chapter 13, Problem 54P

& You fill a 20-cm-tall container with glycerol so that the glycerol (density ${\text{1260**\#x00A0;kg/m}}^{\text{3}}$) reaches the 10-cm mark. You place an oak cube (density ${\text{900 kg/m}}^{\text{3}}$) into the container. Each side of the cube is 10 cm. (a) What is the distance x from the upper face of the cube to the glycerol surface assuming the cube is in an upright position? (b) Make a prediction using qualitative reasoning (without mathematics) about what will happen to the cube in (a) if you now add olive oil (density ${\text{800 kg/m}}^{\text{3}}$) to the container until it is completely full. Will the distance x decrease, increase, or stay the same? (c) Determine the new distance x using mathematics (physics laws) and compare your result with the prediction in (b).