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Physics / Physics with MasteringPhysics 4 / Chapter 15 / Problem 110GP

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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A geode is a hollow rock with a solid shell and an

Chapter 15, Problem 110GP

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QUESTION:

Problem 110GP

A geode is a hollow rock with a solid shell and an air-filled interior. Suppose a particular geode weighs twice as much in air as it does when completely submerged in water. If the density of the solid part of the geode is 2500 kg/m3, what fraction of the geode's volume is hollow?

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QUESTION:

Problem 110GP

A geode is a hollow rock with a solid shell and an air-filled interior. Suppose a particular geode weighs twice as much in air as it does when completely submerged in water. If the density of the solid part of the geode is 2500 kg/m3, what fraction of the geode's volume is hollow?

ANSWER:

Step 1 of 3

We assume that the geode weighs twice as much in air as it does when completely submerged in water.

The weight of the geode submerged in water is half its weight in air, so we wish to calculate the fraction of the volume that is hollow. Set the sum of the force on the geode in water equal to zero and solve for the geodes mass. Because the air is much lighter than the rock, set the mass of the geode equal to the density of the rock times the solid volume.

Hence, the balanced force equation on geode in air is given by

The balanced force equation on geode when submerged in water is given by

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