Which of the following diagrams correctly shows the relation between the terminal velocity vT of a spherical body falling in a liquid and viscosity η of the liquid?

Question

Which of the following diagrams correctly shows the relation between the terminal velocity vT of a spherical body falling in a liquid and viscosity η of the liquid? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

At terminal speed. VT=(2 r2/9 η)(ρS-ρL) g (Assuming other factor constant) So, VT propto (1/η) (rectangular hyperbola)

Q. Which of the following diagrams correctly shows the relation between the terminal velocity $v_{T}$ of a spherical body falling in a liquid and viscosity $η$ of the liquid?

At terminal speed.
$V_{T} = \frac{2 r ^{2}}{9 η} (ρ_{S} - ρ_{L}) g$ (Assuming other factor constant)
So, $V_{T} \propto \frac{1}{η}$ (rectangular hyperbola)

Q. Which of the following diagrams correctly shows the relation between the terminal velocity vT​ of a spherical body falling in a liquid and viscosity η of the liquid?

At terminal speed. VT​=9η2r2​(ρS​−ρL​)g (Assuming other factor constant) So, VT​∝η1​ (rectangular hyperbola)

Q. Which of the following diagrams correctly shows the relation between the terminal velocity $v_{T}$ of a spherical body falling in a liquid and viscosity $η$ of the liquid?

At terminal speed.
$V_{T} = \frac{2 r ^{2}}{9 η} (ρ_{S} - ρ_{L}) g$ (Assuming other factor constant)
So, $V_{T} \propto \frac{1}{η}$ (rectangular hyperbola)