Added mass of a sphere

A sphere of volume $V$ translating through unbounded inviscid incompressible fluid has fluid kinetic energyIts added mass is therefore one half of the displaced fluid mass.

A sphere of density ${\rho }_s$ falling in inviscid fluid of density $\rho$ has effective inertia $({\rho }_s+\rho /2)V$ and net weight $({\rho }_s-\rho )Vg$. Hence