Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 15 - Fluids and Elasticity - Exercises and Problems: 16

Answer

The density of the sphere is $750~kg/m^3$

Work Step by Step

The sum of the sphere's weight and the tension is equal to the buoyant force on the sphere. The buoyant force is equal to the weight of water that is displaced by the sphere. Let $\rho_w$ be the density of water. We can find the volume of the sphere as: $F_B = Mg+T$ $\rho_w~V~g = Mg+\frac{Mg}{3}$ $V = \frac{4M}{3\rho_w}$ We then find the density of the sphere as: $\rho = \frac{M}{V}$ $\rho = \frac{M}{(\frac{4M}{3\rho_w})}$ $\rho = \frac{3\rho_w}{4}$ $\rho = \frac{(3)(1000~kg/m^3)}{4}$ $\rho = 750~kg/m^3$ The density of the sphere is $750~kg/m^3$.
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