Surface Energy

Q. A rectangular film of liquid is extended from $(4\text{cm}\times 2\text{cm})$ to $(5\text{cm}\times 4\text{cm})$. If the work done is $3\times {10}^{-4}\text{J}$, then the value of the surface tension of the liquid is

1. $0.250\text{N/m}$
2. $0.125\text{N/m}$
3. $0.500\text{N/m}$
4. $0.725\text{N/m}$

Q.

$512$ identical drops of mercury are charged to a potential of $2V$ each. The drops are joined to form a single drop. The potential of this drop is ____ $V$.

Q.

$27$ similar drops of mercury are maintained at $10V$each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is _____ times that of a smaller drop.

Q. A certain number of spherical drops of a liquid of radius $r$ each, coalesce to form a single drop of radius $R$ and volume $V$. If $T$ is the surface tension of the liquid, then

1. Energy $=3VT(\frac{1}{r}+\frac{1}{R})$ is released
2. Energy $=3VT(\frac{1}{r}+\frac{1}{R})$ is absorbed
3. Energy $=3VT(\frac{1}{r}-\frac{1}{R})$ is released
4. Energy $=3VT(\frac{1}{r}-\frac{1}{R})$ is absorbed

Q. A spherical liquid drop of radius $R$ is divided into 8 equal droplets. If the surface tension is $T$, then the work done in the process will be:

1. $2\pi R^{2}T$
2. $4\pi R^{2}T$
3. $3\pi R^{2}T$
4. $2\pi R{T}^2$

Q.

A mercury drop of radius $1\text{cm}$ is sprayed into ${10}^6$ droplets of equal size. The energy expended in this process is -

(surface tension of mercury is equal to $32\times {10}^{-2}\text{N/m}$)

1. $0.03\pi \text{J}$
2. $0.01\pi \text{J}$
3. $0.05\pi \text{J}$
4. $0.08\pi \text{J}$

Q. The work done to get $n$ smaller equal size spherical drops from a bigger size spherical drop of water is proportional to:

1. $\left(\frac{1}{n^{2/3}}\right)-1$
2. $\left(\frac{1}{n^{1/3}}\right)-1$
3. $n^{1/3}-1$
4. $n^{4/3}-1$

Q. Determine the energy stored in the surface of a soap bubble of radius $2.1\text{cm}$ if its surface tension is $4.5\times {10}^{-2}\text{N/m}$.

1. $0.6\pi \times {10}^{-4}\text{J}$
2. $1.6\pi \times {10}^{-4}\text{J}$
3. $2.6\pi \times {10}^{-4}\text{J}$
4. $3.6\pi \times {10}^{-4}\text{J}$

Q. Two drops of equal radius coalesce to form a bigger drop. What is the ratio of surface energy of the bigger drop to the smaller drop?

1. $1:1$
2. $2^{2/3}:1$
3. $2^{1/3}:1$
4. $1:2$

Q. If $T$ is the surface tension of a liquid, then the energy needed to break the liquid drop of radius $R$ into $64$ identical drops is

1. $6\pi R^{2}T$
2. $2\pi R^{2}T$
3. $12\pi R^{2}T$
4. $8\pi R^{2}T$

Q. If $T$ is surface tension of the soap solution, then the amount of work done in blowing a soap bubble from diameter $D$ to diameter $2D$ is

1. $4\pi D^{2}T$
2. $6\pi D^{2}T$
3. $2\pi D^{2}T$
4. $8\pi D^{2}T$

Q. Two mercury drops each of radius $r$ merge to form a bigger drop. The surface energy of the bigger drop, if $T$ is the surface tension of mercury, is

1. $2^4\pi r^{2}T$
2. ${\left(\sqrt[3]{32}\right)}^8\pi r^{2}T$
3. $2\pi r^{2}T$
4. ${\left(\sqrt[3]{32}\right)}^4\pi r^{2}T$

Q. A film of water is formed between two straight parallel wires each $10\text{cm}$ long and at separation $0.5\text{cm}$. Calculate the work required to increase $1\text{mm}$ distance between the wires. Surface tension of water$=72\times {10}^{-3}\text{N/m}$.

1. $72\times {10}^{-7}\text{J}$
2. $288\times {10}^{-7}\text{J}$
3. $144\times {10}^{-7}\text{J}$
4. $104\times {10}^{-7}\text{J}$

Q. A rectangular film of liquid is extended from $(4cm\times 2cm)$ to $(5cm\times 4cm)$. If the work done is $3\times {10}^{-4}J$, the value of the surface tension of the liquid is

1. $8.0N/m$
2. $0.250N/m$
3. $0.125N/m$
4. $0.2N/m$

Q.

A drop of liquid of diameter 2.8 mm breaks up into 125 identical drops.

The change in energy is nearly (S.T. of liquid =75 dynes/cm)

1. 19 erg

2. 74 erg

3. 46 erg

4. Zero

Q. Calculate the energy released when $1000$ small water drops each of same radius ${10}^{-7}\text{m}$ coalesce to form one large drop. The surface tension of water is $5\times {10}^{-2}\text{N/m}$.

1. $5\pi \times {10}^{-12}\text{J}$
2. $4.2\pi \times {10}^{-12}\text{J}$
3. $3.6\pi \times {10}^{-12}\text{J}$
4. $1.8\pi \times {10}^{-12}\text{J}$

Q.

A drop of mercury of radius 2 mm is split into 8 identical droplets. Find the increase in surface enery. Surface tension of mercury = $0.465J{m}^{-2}$.

Q. A soap film is formed on a frame of area $4\times {10}^{-3}{\text{m}}^2$. If the area of the film is reduced to half, what is the change in its potential energy?
(Surface tension $=40\times {10}^{-3}\text{N/m}$)

1. $16\times {10}^{-5}\text{J}$
2. $32\times {10}^{-6}\text{J}$
3. $32\times {10}^{-5}\text{J}$
4. $16\times {10}^{-6}\text{J}$

Q. Find the amount of work done in forming a soap film of size $5\text{cm}\times 15\text{cm}$, if surface tension is ${10}^{-2}\text{N/m}$.

1. $1.5\times {10}^{-4}\text{J}$
2. $2\times {10}^{-4}\text{J}$
3. $2.5\times {10}^{-4}\text{J}$
4. $3\times {10}^{-4}\text{J}$

Q. The amount of liquid flowing per second in the tubes $\left(1\right),\left(2\right)$ and $\left(3\right)$ are $10m^3/s,5m^3/s$ and $8m^3/s$ respectively. The velocity of liquid in the tube $\left(4\right)$ having cross - section of $0.5m^2$ is

1. $7m/s$
2. $14m/s$
3. $3.5m/s$
4. $12m/s$

Q. A soap bubble of radius $r_1$ is placed on another soap bubble of radius $r_2(r_1<r_2)$. The radius $R$ of the soap film separating the two bubbles is:

1. $r_1+r_2$
2. $\sqrt{r_1^2+r_2^2}$
3. $(r_1^3+r_2^3)$
4. $\frac{r_2{r}_1}{r_2-r_1}$

Q. A drop of liquid of diameter $2.8\text{mm}$ break up into $216$ identical drops. What is the approximate change in energy of bigger drop?
(Given: Surface tension of liquid, $T=75\text{dyne/cm}$)

1. $25\pi \text{erg}$
2. $32\pi \text{erg}$
3. $28\pi \text{erg}$
4. $29.4\pi \text{erg}$

Q.

In air , a metallic sphere with an internal cavity weighs 40g and in water weighs 20g . the volume of the cavity if the density of material with cavity is 8g/cm^3

Q. The surface energy of a drop of water of radius $r$ is proportional to:

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

Q. If $n$ drops of a liquid, each with surface energy $E$ join to form a single drop, then

1. some energy will be released in the process
2. some energy will be absorbed in the process
3. the energy released will be $E(n^{2/3}-n)$
4. the energy absorbed will be $E(n^{2/3}-n)$

Q. The work done in blowing a soap bubble of $10\text{cm}$ radius is -
(surface tension of soap $=0.03\text{N/m}$).

1. $6.54\times {10}^{-3}\text{J}$
2. $7.54\times {10}^{-3}\text{J}$
3. $8.54\times {10}^{-3}\text{J}$
4. $9.54\times {10}^{-3}\text{J}$

Q. The surface tension of soap solution is $T=0.03{\text{Nm}}^{-1}$. If the size of a soap bubble is increased from a radius of $3\text{cm}$ to $5\text{cm}$, the work done in increasing the size of the soap bubble is

1. $4\pi \text{mJ}$
2. $0.2\pi \text{mJ}$
3. $2\pi \text{mJ}$
4. $0.4\pi \text{mJ}$

Q. Work done on a liquid drop to increase its radius from $3\text{cm}$ to $5\text{cm}$ is $\pi \times {10}^{-4}\text{J}$. Find the surface tension of liquid.

1. $\frac{1}{8}\text{N/m}$
2. $\frac{1}{4}\text{N/m}$
3. $\frac{1}{32}\text{N/m}$
4. $\frac{1}{64}\text{N/m}$

Q.

Find the excess pressure inside (a) a drop of mercury of radius 2 mm (b) a soap bubble of radius 4 mm and (c) an air bubble of radius 4 mm formed inside a tank of water. Surface tension of mercury , soap solution and water are $0.46N{m}^{-1},0.03N{m}^{-1}$ and $0.076N{m}^{-1}$ respectively.

Q. Work of $3\times {10}^{-4}\text{J}$ is required to be done in increasing the size of a soap film from $10\text{cm}\times 6\text{cm}$ to $10\text{cm}\times 11\text{cm}$. The surface tension of the film is

1. $5\times {10}^{-2}\text{N/m}$
2. $3\times {10}^{-2}\text{N/m}$
3. $2\times {10}^{-2}\text{N/m}$
4. $4\times {10}^{-2}\text{N/m}$