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What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one -half that of a freely falling body? (The densities of metal and of liquid are \[\rho \] and \[\sigma \] respectively, and the viscosity of the liquid is \[\eta \]).

A) \[\frac{{{r}^{2}}g}{9\eta }(\rho -2\sigma )\]

B) \[\frac{{{r}^{2}}g}{9\eta }(2\rho -\sigma )\]

C) \[\frac{{{r}^{2}}g}{9\eta }(\rho -\sigma )\]

D) \[\frac{2{{r}^{2}}g}{9\eta }(\rho -\sigma )\]