A small ball of mass $M$, radius $R$ and density $\rho$ moves with terminal velocity through a container…
A small ball of mass $M$, radius $R$ and density $\rho$ moves with terminal velocity through a container filled with glycerine of density $\sigma$. The viscous force acting on the ball is ( $g=$ gravitational acceleration)
Мgрб
$M g(\rho-\sigma)$
$M g\left[1-\frac{\sigma}{\rho}\right]$
$\frac{M g \rho}{\sigma}$
Solution
Considering force balance on the ball falling with terminal velocity:
$F_v+\sigma V g=\rho V g$
where $F_v$ is the viscous force, $V$ is the volume of the ball.
Taking the ratio of equation (1) and (2):
$F_v=M g\left(1-\frac{\sigma}{\rho}\right)$
Taking the ratio of equation (1) and (2):
$F_v=M g\left(1-\frac{\sigma}{\rho}\right)$