Stokes Law

A spherical ball of radius $\text{1}\times 10^{-4} \mathrm{m}$ and density $104 \mathrm{kg} {\mathrm{m}}^{-3}$^​ falls freely under gravity through a distance $h$ before entering a tank of water. If after entering the water the velocity of the ball does not change, find $h$. The viscosity of water is $9.8\times 10^{-6} {\mathrm{Nsm}}^{-2}$.

The constant velocity of the raindrop is because of _____.

A raindrop falling in air is similar to motion of what kind of body in viscous medium?

Falling rain drops velocity vary with the height with respect to the surface.

Stoke's can be applied for the measurement of the viscosity of fluids

List the applications of Stokes Law.

A lead ball of $1 \mathrm{mm}$ diameter falls through a long column of glycerine. The variation of its velocity with distance covered is represented by

A cylinder of mass $M$ and radius $R$ moves with constant speed $v$ through a region of space that contains dust particles of mass $m$ which are at rest. There are $n$ number of particles per unit volume. The cylinder moves in a direction perpendicular to its axis. Assume $m<<M$ and that the particles do not interact with each other. All the collisions taking place are perfectly elastic and the surface of the cylinder is smooth. The drag force per unit length of the cylinder required to maintain a speed $v$ constant for the cylinder when it has entered a region is $\frac{K}{3}nmR{v}^2$. Find the value of $K$.

Two balls of radii $r$ and $\frac{r}{2}$ are released inside a deep water tank. Their initial accelerations are found to be $g/2$ and $g/4$ respectively. If the velocity of smaller ball relative to the larger ball a long time after the two balls are released is $\frac{{\mathit{Pr}}^2\rho g}{\eta }$ upwards. If $P$ is $\frac{20}{x}$ then find $x$. (Coefficient of viscosity of liquid is $\eta$ and density of liquid is $\rho$).

Eight identical drops of water, each of radius $2 \mathrm{mm}$ are falling through air at a terminal velocity of $8 \mathrm{cm} {\mathrm{s}}^{-1}$. If they coalesce to form a single drop, then the terminal velocity of the combined drop will be :

Best graph from following between terminal velocity $\left(\mathrm{v}\right)$ of a spherical object and radius of object $\left(\mathrm{r}\right)$ is 

In Millikan's oil drop experiment, what is the terminal speed of an unchanged drop of the radius of $2.0\times {10}^{-5} \mathrm{m}$ and the density $1.2\times {10}^{23} \mathrm{kg} {\mathrm{m}}^{-3}$? Take the viscosity of air at the temperature of the experiment to be $1.8\times {10}^{-5} \mathrm{Pa}-\mathrm{s}$. The viscous force on the drop at that speed is $n\times {10}^{-10} \mathrm{N}$. What is the value of $n$?

(Write $n$ to the nearest integer & neglect buoyancy of the drop due to air)

A drop of water of radius $0.0015 \mathrm{m}\mathrm{m}$ is falling in air. If the coefficient of viscosity of air is $2.0\times {10}^{-5} \mathrm{k}\mathrm{g}\mathrm{ }{\mathrm{m}}^{-1} {\mathrm{s}}^{-1}$, the terminal velocity of the drop will be: (The density of water $={10}^3 \mathrm{k}\mathrm{g}\mathrm{ }{\mathrm{m}}^{-3}$ and $\mathrm{g}=10 \mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}$)

Eight drops of water, each of radius $2 \mathrm{m}\mathrm{m}$ are falling through air at a terminal velocity of $8 \mathrm{c}\mathrm{m}\mathrm{ }{\mathrm{s}}^{-1}$. If they coalesce to from a single drop, then the terminal velocity of combined drop will be:

A metallic sphere of mass $M$ falls through glycerine, If we drop a ball of mass$8M$ of same metal into a column of glycerine, the terminal velocity of the ball will be

A spherical ball of radius $\mathrm{R}$ is falling in a viscous fluid with velocity $\mathrm{v}$. The retarding viscous force acting on the spherical ball is:

A copper ball of radius $r$ is moving with a uniform velocity $v$ in the mustard oil and the dragging force acting on the ball is $F.$ The dragging force on the copper ball of radius $2r$ with uniform velocity $2v$ in the mustard oil is

A rain drop of radius $0.3 mm$ has a terminal velocity in air $1 m{s}^{-1}.$ The viscosity of air is $18\times {10}^{-5}$ poise. Find the viscous force on the rain drops.

What will be the approximate terminal velocity of a rain drop of diameter $1.8\times {10}^{-3}m$ , when density of rain water $\approx {10}^{3}kg{m}^{-3}$ and the coefficient of viscosity of air $\approx 1.8\times {10}^{-5}N-s{m}^{-2}$ ? $\left(\mathrm{N}\mathrm{e}\mathrm{g}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{ }\mathrm{b}\mathrm{u}\mathrm{o}\mathrm{y}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{y}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{a}\mathrm{i}\mathrm{r}\right)$

Two spheres of radii ${\mathrm{r}}_1$ and ${\mathrm{r}}_2\mathrm{ }({\mathrm{r}}_1\mathrm{ }>\mathrm{ }{\mathrm{r}}_2)$ is dropped through a tube full of glycerine. Their terminal velocities ${\mathrm{v}}_1$ and ${\mathrm{v}}_2$ are calculated in the experiment. Which of the following is true?