Chapter 14, Problem 34AP

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 ρ. Representing the density of air as ρ_air and the balance reading as ${F^{\prime }}_g$, show that the true weight F_g is

$F_g={F^{\prime }}_g+\left(V-\frac{{F^{\prime }}_g}{\rho g}\right){\rho }_{air}g$