What is the velocity $v$ of a metallic ball of radius $r$ falling in a tank of liquid at the instant

Question

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 if metal and of liquid are $ho$ and $\sigma$ respectively, and the viscosity of the liquid in $\eta$ )\

Professor PC Thomas Classes · Answer

$\frac{4}{3} \pi \mathrm{R}^{3}(ho-\sigma) \mathrm{g}-6 \pi \eta \mathrm{rv}=\frac{4}{3} \pi \mathrm{R}^{3} ho \frac{\mathrm{~g}}{2}$\ $6 \pi \eta \mathrm{rv}=\frac{4}{3} \pi \mathrm{r}^{3}\left(\frac{ho}{2}-\sigmaight) \mathrm{g}$\ $v=\frac{r^{2}}{9 \eta}(ho-2 \sigma) g$\