Physics - Fluid Question with Solution | TestHub

The ball is moving with constant velocity. Hence the net force acting on it is zero. The weight of the ball, $\mathrm{W}=\frac{4}{3}\pi {\mathrm{r}}^3{\rho }_{\mathrm{b}}\mathrm{g}$ (in downward direction) The viscous force $F_v$ is in downward direction The buoyant force ${\mathrm{F}}_{\mathrm{B}}=\frac{4}{3}\pi {\mathrm{r}}^3{\rho }_{\ell }$ g (in upward direction) $$\begin{array}{rl}& \therefore {\mathrm{F}}_{\mathrm{v}}+\mathrm{W}={\mathrm{F}}_{\mathrm{B}}\\ & \therefore {\mathrm{F}}_{\mathrm{v}}={\mathrm{F}}_{\mathrm{B}}-\mathrm{W}\\ & =\frac{4}{3}\pi {\mathrm{r}}^3\mathrm{g}\left({\rho }_{\ell }-{\rho }_{\mathrm{b}}\right)=\frac{4}{3}\pi {\mathrm{r}}^3\mathrm{g}\times 3{\rho }_{\mathrm{b}}\left(\because {\rho }_{\ell }=4{\rho }_{\mathrm{b}}\right)\\ & \therefore \frac{{\mathrm{F}}_{\mathrm{v}}}{\mathrm{W}}=3\end{array}$$