A cubical block of density and with sides of length L

Chapter 12, Problem 12.83

(choose chapter or problem)

A cubical block of density \(\rho_{\mathrm{B}}\) and with sides of length L floats in a liquid of greater density \(\rho_{\mathrm{L}}\). (a) What fraction of the block’s volume is above the surface of the liquid? (b) The liquid is denser than water (density \(\rho_{\mathrm{W}}\)) and does not mix with it. If water is poured on the surface of the liquid, how deep must the water layer be so that the water surface just rises to the top of the block? Express your answer in terms of L, \(\rho_{\mathrm{B}}\), \(\rho_{\mathrm{L}}\), and \(\rho_{\mathrm{W}}\). (c) Find the depth of the water layer in part (b) if the liquid is mercury, the block is made of iron, and the side length is 10.0 cm.

Text Transcription:

rho_B

rho_L

rho_W