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

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 14 - Fluids and Elasticity - Exercises and Problems: 19

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 can 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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