## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson

# Chapter 14 - Fluids and Elasticity - Conceptual Questions: 1

#### Answer

(a) The density does not change. (b) The density decreases by a factor of 8.

#### Work Step by Step

$density = \frac{mass}{volume}$ $\rho = \frac{M}{V}$ (a) Density depends on the material. If the type of material does not change, then the density does not change. If the volume increases by a factor of 8, then the mass will also increase by a factor of 8 since the material is the same. Therefore, the density does not change. $\rho^* = \frac{8M}{8V} = \frac{M}{V} = \rho$ (b) If each of the object's three dimensions is increased by a factor of 2, then the volume increases by a factor of 8. Since the mass does not change, then the density decreases by a factor of 8. $\rho' = \frac{M}{8V} = \frac{\rho}{8}$

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