Terminal Velocity

Q. A sphere of radius $R$ and density ${\rho }_1$ is dropped in a liquid of density $\sigma$. Its terminal velocity is $v_1$ . If another sphere of radius $R$ and density ${\rho }_2$ is dropped in the same liquid, its terminal velocity will be:

1. $\left(\frac{{\rho }_2-\sigma }{{\rho }_1-\sigma }\right)v_1$
2. $\left(\frac{{\rho }_1-\sigma }{{\rho }_2-\sigma }\right)v_1$
3. $\left(\frac{{\rho }_1}{{\rho }_2}\right)v_1$
4. $\left(\frac{{\rho }_2}{{\rho }_1}\right)v_1$

Q. A spherical ball is dropped in a long column of a viscous liquid. The speed of the ball as a function of time may be best represented by the graph

1. A
2. B
3. C
4. D

Q. Two spherical rain drops with radii in the ratio $1:2$ fall from a great height through the atmosphere. The ratio of their momenta after they have attained terminal velocity is:

1. $1:8$
2. $2:1$
3. $1:32$
4. $1:2$

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

1. directly proportional to $R$ but inversely proportional to $v$
2. directly proportional to both radius $R$ and velocity $v$
3. inversely proportional to both radius $R$ and velocity $v$
4. inversely proportional to $R$ but directly proportional to velocity $v$

Q. Eight equal drops of water are falling through air with a steady velocity of $5\text{cm/sec}$. If smaller drops combine to form a single large drop, then the terminal velocity (in $\text{cm/sec}$) of this large drop is

1. $5$
2. $20$
3. $10$
4. $15$

Q. A small spherical body of radius $r$ is falling under gravity in a viscous medium and due to friction, the medium gets heated. When the body attains terminal velocity, then the rate of heating is proportional to:

1. $r$
2. $r^{3/2}$
3. $r^5$
4. $r^{1/2}$

Q. A small sphere of radius $r$ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

1. $r^3$
2. $r^2$
3. $r^5$
4. $r^4$

Q.

What does fluid flow mean?

Q. A small sphere of radius $r$ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

1. $r^3$
2. $r^2$
3. $r^5$
4. $r^4$

Q. A small spherical body of radius $r$ is falling under gravity in a viscous medium and due to friction, the medium gets heated. When the body attains terminal velocity, then the rate of heating is proportional to:

1. $r$
2. $r^{3/2}$
3. $r^5$
4. $r^{1/2}$

Q. Find the terminal velocity of a free falling water drop of radius $0.04\text{mm}$:-
The coefficient of viscosity of air is $1.9\times {10}^{-5}{\text{Ns/m}}^2$ and its density is $1.2{\text{kg/m}}^3$. Density of water is $1000{\text{kg/m}}^3$. Take $g=10{\text{m/s}}^2$.

1. $15\text{cm/s}$
2. $19\text{cm/s}$
3. $2.5\text{cm/s}$
4. $13\text{cm/s}$

Q. Eight small drops of equal size are falling through air with a steady velocity of $10\text{cm/sec}$. If the drops coalesce, what would be the terminal velocity of the bigger drop?

1. $40\text{cm/s}$
2. $20\text{cm/s}$
3. $30\text{cm/s}$
4. $50\text{cm/s}$

Q. Ratio of viscosities and densities of two liquids flowing in similar tubes are 52:49 and 13:1 respectively.

1. The ratio of their critical velocities is 4 : 49
2. The ratio of their critical velocities is 49 : 4
3. The ratio of their critical velocities is 2 : 7

4. The ratio of their critical velocities is 7 : 2

Q. The ratio of the terminal velocities of two drops of same density of radii $R$ and $R/2$ in air is

1. $2$
2. $1$
3. $1/2$
4. $4$

Q. A spherical ball of mass $4m$, density $\sigma$ and radius $r$ is attached to a pulley-mass system as shown in the figure. The ball is released in a beaker with a liquid of coefficient of viscosity $\eta$ and density $\rho (<\frac{\sigma }{2})$. If the length of the liquid column in the beaker is sufficiently long, the terminal velocity attained by the ball is given by: (Assume all pulleys to be massless and strings to be massless and inextensible):

1. $\frac{2}{9}\frac{r^2(2\sigma -\rho )g}{\eta }$
2. $\frac{r^2(\sigma -2\rho )g}{9\eta }$
3. $\frac{2}{9}\frac{r^2(\sigma -4\rho )g}{\eta }$
4. $\frac{2}{9}\frac{r^2(\sigma -3\rho )g}{\eta }$

Q. A sphere of mass $m$ and radius $r$ is projected along a straight line in a gravity free space with speed $v$. If the coefficient of viscosity of the medium in which it moves is $\frac{1}{6\pi }$, then the distance travelled by the body before it stops is

1. $\frac{mv}{2r}$
2. $\frac{2mv}{r}$
3. $\frac{mv}{r}$
4. $\frac{mv}{4r}$

Q. A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in the figure, indicate the one that represents the velocity $\left(v\right)$ of the pebble as a function of time $\left(t\right)$.

1. 
2. 
3. 
4. 

Q.

A rain drop falls near the surface of the Earth with almost uniform velocity because

1. Its weight is negligible

2. The force of surface tension balances its weight

3. The force of viscosity of air balances its weight

4. The drops are charged and atmospheric electric field balances its weight

Q. A $50\text{kg}$ skydiver falls through the air and attains terminal velocity after some time. The drag force is a function of velocity given as $F_{\text{drag}}=-b{v}^2$ where the negative sign denotes that the drag force is opposite to the direction of velocity. What is the terminal velocity of the skydiver (assuming the drag constant $b$ is $0.2\text{kg/m})$?

1. $5\text{m/s}$
2. $50\text{m/s}$
3. $100\text{m/s}$
4. $250\text{m/s}$

Q. Two equal drops of water are falling through air with a steady velocity $v$. If the drops coalesce, the new velocity will be

1. $2v$
2. $\sqrt{2}v$
3. $2^{2/3}v$
4. $\frac{v}{\sqrt{2}}$

Q. A small sphere of density $\rho$ falls from rest into a viscous liquid of density $\sigma$ and viscosity $\eta$. Due to friction, heat is produced. Which of the follwing options correctly represents the relation between the rate of production of heat $H$ and the radius of the sphere $r$ at terminal velocity?

1. $\frac{12\pi (\rho -\sigma )g^2{r}^5}{27\eta }$
2. $\frac{12\pi (\rho -\sigma {)}^2{g}^2{r}^5}{27\eta }$
3. $\frac{8\pi (\rho -\sigma )g^2{r}^5}{27\eta }$
4. $\frac{8\pi (\rho -\sigma {)}^2{g}^2{r}^5}{27\eta }$

Q. A small spherical body of radius $r$ is falling under gravity in a viscous medium and due to friction, the medium gets heated. When the body attains terminal velocity, then the rate of heating is proportional to:

1. $r$
2. $r^{3/2}$
3. $r^5$
4. $r^{1/2}$

Q. An oil drop falls through air with a terminal velocity of $5\times {10}^{-4}\text{m/s}$. The radius of the drop will be:

Neglect density of air compared to that of oil. (Viscosity of air $=\frac{18\times {10}^{-5}}{5}{\text{N.s/m}}^2,g=10{\text{m/s}}^2$, density of oil $=900{\text{kg/m}}^3$

1. $2.5\times {10}^{-6}\text{m}$
2. $2\times {10}^{-6}\text{m}$
3. $3\times {10}^{-6}\text{m}$
4. $4\times {10}^{-6}\text{m}$

Q. An oil drop falls through air with a terminal velocity $5\times {10}^{-4}\text{m/s}$. Find the radius of the drop.
Neglect the density of air as compared to that of oil. (Take viscosity of air $=3.6\times {10}^{-5}{\text{N-s/m}}^2,g=10{\text{m/s}}^2$, density of oil ${\rho }_o=900{\text{kg/m}}^3)$

1. $2\times {10}^{-6}\text{m}$
2. $2.5\times {10}^{-6}\text{m}$
3. $4\times {10}^{-6}\text{m}$
4. $3\times {10}^{-6}\text{m}$

Q. A rain drop falls near the surface of the earth with almost uniform velocity because the force of viscosity of air balances its weight.

1. False
2. True

Q. If the terminal speed of a sphere of gold (density $=19.5{\text{kg/m}}^3$) is $0.2\text{m/s}$ in a viscous liquid (density $=1.5{\text{kg/m}}^3$), find the terminal speed of a sphere of silver (density $=10.5{\text{kg/m}}^3$) of the same size in the same liquid

1. $0.4\text{m/s}$
2. $0.133\text{m/s}$
3. $0.1\text{m/s}$
4. $0.2\text{m/s}$

Q. If the terminal speed of a sphere of gold (density = $19.5{\text{g/cm}}^3)$ is $0.2\text{m/s}$ in a viscous liquid (density = $1.5{\text{g/cm}}^3$). Find the terminal speed of a sphere of silver (density $=10.5{\text{g/cm}}^3)$ of the same size in the same liquid.

1. $0.4\text{m/s}$
2. $0.3\text{m/s}$
3. $0.25\text{m/s}$
4. $0.1\text{m/s}$

Q.

A piece of wood is taken deep inside a long column of water and released it will move up

1. With a constant upward acceleration

2. With a decreasing upward acceleration

3. With a decelaration

4. With a uniform velocity

Q. The ratio of the terminal velocities of two drops of same density of radii $R$ and $R/2$ in air is

1. $2$
2. $1$
3. $1/2$
4. $4$

Q. A small sphere of density $\rho$ falls from rest into a viscous liquid of density $\sigma$ and viscosity $\eta$. Due to friction, heat is produced. Which of the follwing options correctly represents the relation between the rate of production of heat $H$ and the radius of the sphere $r$ at terminal velocity?

1. $\frac{12\pi (\rho -\sigma )g^2{r}^5}{27\eta }$
2. $\frac{12\pi (\rho -\sigma {)}^2{g}^2{r}^5}{27\eta }$
3. $\frac{8\pi (\rho -\sigma )g^2{r}^5}{27\eta }$
4. $\frac{8\pi (\rho -\sigma {)}^2{g}^2{r}^5}{27\eta }$