The velocity of a small ball of mass ' $M$ ' and density ' $\mathrm{d}_1$ ' when dropped in a container…
The velocity of a small ball of mass ' $M$ ' and density ' $\mathrm{d}_1$ ' when dropped in a container filled with glycerin becomes constant after some time. If the density of glycerin is ' $\mathrm{d}_2$ ', the viscous force acting on the ball is ( $\mathrm{g}$ = acceleration due to gravity)
Since the velocity is constant, the net force acting on the ball is zero.
$\begin{aligned}
& \mathrm{F}_{\mathrm{V}}+\mathrm{F}_{\mathrm{B}}=\mathrm{Mg} \\
& \mathrm{F}_{\mathrm{V}}+\mathrm{Vd}_2 \mathrm{~g}=\mathrm{Mg}
\end{aligned}$
$\mathrm{F}_{\mathrm{v}}+\frac{\mathrm{M}}{\mathrm{d}_1} \mathrm{~d}_2 \mathrm{~g}=\mathrm{Mg}$
$\mathrm{F}_{\mathrm{V}}=\mathrm{Mg}\left(1-\frac{\mathrm{d}_2}{\mathrm{~d}_1}\right)$