Surface tension

A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is $\alpha\times10^{-6}$ J. The value of $\alpha$ is ________. (Take surface tension of liquid = 0.08 N/m)

The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is $\alpha\pi\times10^{-4}$ J. The value of $\alpha$ is ________. (Take $\pi=3.14$)

The surface tension of a soap solution is $3.5\times10^{-2}$ N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is $\alpha\times10^{-6}$ J. The value of $\alpha$ is ________. ($\pi=22/7$)

Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is ________. ($S$ is the surface tension of mercury).

A spherical soap bubble inside an air chamber at pressure $P_0 = 10^5\,\mathrm{Pa}$ has a certain radius so that the excess pressure inside the bubble is $\Delta P = 144\,\mathrm{Pa}$. Now, the chamber pressure is reduced to $8P_0/27$ so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure $\Delta P$ in both the cases to be much smaller than the chamber pressure. The new excess pressure $\Delta P$ in Pa is _____.

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius 0.1 mm is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The air in the container is isothermally compressed from its original volume $V_0$ to $\dfrac{100}{101}V_0$ with the movable piston. Considering air as an ideal gas, the height $(h)$ of the liquid column in the capillary above the liquid level in cm is _____.

[Given: Surface tension of the liquid is $0.075\ \mathrm{N\,m^{-1}}$, atmospheric pressure is $10^5\ \mathrm{N\,m^{-2}}$, acceleration due to gravity $(g)$ is $10\ \mathrm{m\,s^{-2}}$, density of the liquid is $10^3\ \mathrm{kg\,m^{-3}}$ and contact angle of capillary surface with the liquid is zero]

A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma = \dfrac53$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a1}$, the radius of the bubble is found to be $r_1$ and the temperature of the enclosed gas is $T_1$. When the atmospheric pressure is $P_{a2}$, the radius of the bubble and the temperature of the enclosed gas are $r_2$ and $T_2$, respectively.

Which of the following statement(s) is(are) correct?

A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be :

The excess pressure inside a liquid drop is 500 Nm$^{-2}$. If the radius of the drop is 2 mm, the surface tension of liquid is $x\times10^{-3}$ Nm$^{-1}$. The value of $x$ is ______.

A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5\times10^{-4}$ Ncm$^{-1}$. The radius of drop in cm will be : ($g=10$ ms$^{-2}$)

A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be :

(Given $\pi=3.14$)

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is ______.

Given below are two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).

Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is ρ and radius of the drop is r, then $T=K\sqrt{\dfrac{\rho r^3}{S^{3/2}}}$ is dimensionally correct, where K is dimensionless.

Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.

In the light of above statements, choose the correct answer from the options given below.

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Clothes containing oil or grease stains cannot be cleaned by water wash.

Reason (R) : Because the angle of contact between the oil/grease and water is obtuse.

In the light of the above statements, choose the correct answer from the option given below.

A water drop of radius 1 cm is broken into eight equal droplets. Surface tension of water is 0.075 N m$^{-1}$. The gain in surface energy is _______ $\times10^{-7}$ J. (Take π = 3.14)

When water is filled carefully in a glass, one can fill it to a height $h$ above the rim of the glass due to the surface tension of water. To calculate $h$ just before water starts flowing, model the shape of the water above the rim as a disc of thickness $h$ having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the rim and water starts flowing from there. If the density of water, its surface tension and the acceleration due to gravity are $10^3\ \mathrm{kg\,m^{-3}}$, $0.07\ \mathrm{N\,m^{-1}}$ and $10\ \mathrm{m\,s^{-2}}$, respectively, the value of $h$ (in mm) is ______.

A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T1 and T2 of different materials having water contact angles of 0° and 60°, respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in figure. Which of the following option(s) is(are) correct?

[Surface tension of water = 0.075 N/m, density of water = 1000 kg/m³, take $g = 10\ \mathrm{m/s^2}$]

A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$. The angle of contact between water and the wall of the capillary tube is $\theta$. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

A drop of liquid of radius $R = 10^{-2}$ m having surface tension $S = \frac{0.1}{4\pi}\ \mathrm{Nm^{-1}}$ divides itself into $K$ identical drops. In this process the total change in the surface energy $\Delta U = 10^{-3}$ J. If $K = 10^\alpha$ then the value of $\alpha$ is

If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by :