Physics - Fluid Question with Solution | TestHub

Given: Mass of sphere $=\mathrm{m}$, Density of sphere $={\sigma }_1$, Density of liquid $={\sigma }_2$. $\mathrm{At}=\mathrm{v}={\mathrm{v}}_{\mathrm{t}}$, Weight of sphere $(\mathrm{W})=$ Viscous Force $\left({\mathrm{F}}_{\mathrm{V}}\right)+$ Buoyant Force due to the medium $\left({\mathrm{F}}_{\mathrm{B}}\right)$ $\begin{array}{rl}\Rightarrow \mathrm{W}& ={\mathrm{F}}_{\mathrm{V}}+{\mathrm{F}}_{\mathrm{B}}\\ \mathrm{Mg}& ={\mathrm{F}}_{\mathrm{V}}+\left({\sigma }_2\mathrm{V}\right)\mathrm{g}\dots .(\because \mathrm{m}=\mathrm{D}.\mathrm{V})\\ \therefore {\mathrm{F}}_{\mathrm{V}}& =\mathrm{mg}-\left({\sigma }_2\mathrm{V}\right)\mathrm{g}\\ & =\mathrm{mg}\left[1-\frac{{\sigma }_2\mathrm{V}}{\mathrm{m}}\right]\\ & =\mathrm{mg}\left[1-\frac{{\sigma }_2\mathrm{V}}{{\sigma }_1\mathrm{V}}\right]\\ & =\mathrm{mg}\left[1-\frac{{\sigma }_2}{{\sigma }_1}\right]\end{array}$