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

  $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}(\mathrm{\rho }-2\mathrm{\sigma })$

• B

  $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}(2\mathrm{\rho }-\mathrm{\sigma })$

• C

  $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}(\mathrm{\rho }-\mathrm{\sigma })$

• D

  $\frac{2{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}(\mathrm{\rho }-\mathrm{\sigma })$