JEE Surface Tension PYQs With Video Solutions, Download PDF

A small spherical droplet of density $$d$$ is floating exactly half immersed in a liquid of density $$\rho$$ and surface tension $$T$$. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet):

The ratio of surface tensions of mercury and water is given to be 7.5, while the ratio of their densities is 13.6. Their contact angles, with glass, are close to 135° and 0°, respectively. If it is observed that mercury gets depressed by an amount $$h$$ in a capillary tube of radius $$r_1$$, while water rises by the same amount $$h$$ in a capillary tube of radius $$r_2$$, then the ratio $$\frac{r_1}{r_2}$$ is close to

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is:

A capillary tube is immersed vertically in water and the height of the water column is $$x$$. When this arrangement is taken into a mine of depth d, the height of the water column is $$y$$. If R is the radius of earth, the ratio $$\frac{x}{y}$$ is:

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement-1: A capillary is dipped in a liquid and liquid rises to a height h in it. As the temperature of the liquid is raised, the height h increases (if the density of the liquid and the angle of contact remain the same).
Statement-2: Surface tension of a liquid decreases with the rise in its temperature.

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

A big drop is formed by coalescing 1000 small identical drops of water. If $$E_1$$ be the total surface energy of 1000 small drops of water and $$E_2$$ be the surface energy of single big drop of water, the $$E_1 : E_2$$ is $$x : 1$$, where $$x$$ = ________.

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $$R$$ = Radius of bubble, $$S$$ = Surface tension of bubble)

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises uptocertain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1 % each, then the height of the liquid in the tube will change by __ %.

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is $$n$$ times the volume of the bubble B, then the value of n is ________.

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If $$r \ll R$$, and the surface tension of water is T, value of r just before bubbles detach is: (density of water is $$\rho_w$$)

An air bubble of volume 2.9 $$cm^{3}$$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is $$17^{o}$$C. The volume of the bubble when it reaches the surface, where the water temperature is $$27^{o}$$C, is ______$$cm^{3}$$.
($$g = 10 m/s^{2}$$, density of water = $$10^{3} kg/m^{3}$$, and 1 atm pressure is $$10^{5}$$ Pa)

Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the unwaxed capillary, the angle of contact $$\theta$$ and the height $$h$$ upto which water rises change. These changes are :

A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 N m$$^{-1}$$, density = 667 kg m$$^{-3}$$) which rises to height h in the tube. It is observed that the two tangents drawn from observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60$$°$$ with one another. Then h is close to (g = 10 m s$$^{-2}$$):

When two soap bubbles of radii $$a$$ and $$b$$ ($$b > a$$) coalesce, the radius of curvature of common surface is:

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid $$A$$ vertically is, $$5$$ cm. If the tube is dipped in a similar manner in another liquid $$B$$ of surface tension and density double the values of liquid $$A$$, the height of liquid column raised in liquid B would be ______ m.

If two glass plates have water between them and are separated by very small distance (see the figure below), 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:

If 1000 droplets of water of surface tension 0.07 N m$$^{-1}$$, having same radius 1 mm each, combine to form a single drop. In the process the released surface energy is- (Take $$\pi = \dfrac{22}{7}$$)

A mercury drop of radius $$10^{-3}$$ m is broken into 125 equal size droplets. Surface tension of mercury is 0.45 N m$$^{-1}$$. The gain in surface energy is:

There is an air bubble of radius $$1.0$$ mm in a liquid of surface tension $$0.075$$ N m$$^{-1}$$ and density $$1000$$ kg m$$^{-3}$$ at a depth of $$10$$ cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _____ Pa ($$g = 10$$ m s$$^{-2}$$).

The surface tension of a soap solution is $$3.5 \times 10^{-2}$$ N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is $$\alpha \times 10^{-6}$$ J. The value of $$\alpha$$ is _____. $$(\pi = 22/7)$$

A $$20$$ cm long capillary tube is dipped in water. The water rises up to $$8$$ cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

If two soap bubbles of different radii are connected by a tube,

Work done in increasing the size of a soap bubble from a radius of $$3 \, \text{cm}$$ to $$5 \, \text{cm}$$ is nearly (Surface tension of soap solution $$= 0.03 \, \text{Nm}^{-1}$$):

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $$1.5 \times 10^{-2}$$ N (see figure). The length of the slider is $$30$$ cm and its weight negligible. The surface tension of the liquid film is

A large number of droplets, each of radius $$r$$ coalesce to form a bigger drop of radius $$R$$. An engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is ($$T$$ = surface tension, $$\rho$$ = density)

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle $$\simeq 0^\circ$$) with $$30^\circ$$ inclined with vertical. The length of water risen in the capillary is _____ cm. (Take $$g = 9.8$$ m/s$$^2$$)

Two water drops each of radius 'r' coalesce to form a bigger drop. If 'T' is the surface tension, the surface energy released in this process is :

Two liquids A and B have $$\theta_A$$ and $$\theta_B$$ as contact angles in a capillary tube. If $$K = \cos\theta_A / \cos\theta_B$$, then identify the correct statement: