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Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
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A cubical block of density ?B and with sides of length L

Chapter 12, Problem 83P

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QUESTION:

Problem 83P

A cubical block of density ρB and with sides of length L floats in a liquid of greater density ρL. (a) What fraction of the block’s volume is above the surface of the liquid? (b) The liquid is denser than water (density ρW) and does not mix with it. If water is poured on the surface of that 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 , ρB, ρL, and ρW. (c) Find the depth of the water layer in part (b) if the liquid is mercury, the block is made of iron, and L = 10.0 cm.

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QUESTION:

Problem 83P

A cubical block of density ρB and with sides of length L floats in a liquid of greater density ρL. (a) What fraction of the block’s volume is above the surface of the liquid? (b) The liquid is denser than water (density ρW) and does not mix with it. If water is poured on the surface of that 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 , ρB, ρL, and ρW. (c) Find the depth of the water layer in part (b) if the liquid is mercury, the block is made of iron, and L = 10.0 cm.

ANSWER:

Solution 83P

Step 1 of 3:

Introduction

Archimedes principle states that the buoyant force exerted on an object by the liquid is equal to the weight of water displaced by the object.

According to the Archimedes principle, the buoyant force exerted on an object by the liquid is equal to the weight of water displaced by the object.

For the part submerged in water,

Here, V is the volume submerged in water and V0 is the original volume.

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