Serway & Jewett — Fluid Mechanics: Problem 34

The true weight of an object can be measured in a vacuum, where buoyant forces are absent. A measurement in air, however, is disturbed by buoyant forces. An object of volume \( V \) is weighed in air on an equal-arm balance with the use of counterweights of density \( \rho \). Representing the density of air as \( \rho_{air} \) and the balance reading as \( F'_g \), show that the true weight \( F_g \) is \[ F_g = F'_g + \left(V - \frac{F'_g}{\rho g}\right) \rho_{air} g \]