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Two bubbles of each of radius R are in contact with each other. What is the radius of curvature of circular perimeter of soap film that separates two bubbles? Both the bubbles have same surface tension.

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Important Questions on Mechanical Properties of Fluids

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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
A soap bubble having radius of 1 mm is blown from a detergent solution having a surface tension of 2.5×10-2 N m-1. The pressure inside the bubble equals at a point Z0 below the free surface of water in a container. Taking g=10 m s-2, density of water =103 kg m-3, the value of Z0 is
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
Two soap bubbles of radii 3 mm and 4 mm confined in vacuum coalesce isothermally to form a new bubble. The radius of the bubble formed in mm is
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
A glass capillary tube is of the shape of a truncated cone with an apex angle α so that its two ends have cross-sections of different radii. When dipped in water vertically, the water rises in it to a height h, where the radius of its cross-section is b. If the surface tension of water is S, its density is ρ, and its contact angle with glass is θ, then the value of h will be (g is the acceleration due to gravity)

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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
Work done in increasing the size of a soap bubble from radius of (3 to 5) cm is nearly (surface tension of soap solution =0.03 N m-1)
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
A large number of liquid drops each of radius r coalesce to form a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (Surface tension of liquid T, Density ρ)
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
A large number of liquid drops each of radius r coalesce to form a single drop of the radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of the liquid T, density ρ)
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be:
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
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, is
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
A big water drop is formed by the combination of n small water drops of equal radii. The ratio of the surface energy of n drops to the surface energy of the big drop is
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
Two separate soap bubbles of radii 3×10-3 m and 2×10-3 m respectively, formed of same liquid (surface tension 65×10-2 N m-1) come together to form a double bubble. The radius of interface of double bubble is
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension

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:

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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
The surface tension of the soap water solution is 110πN m-1. The free energy of the surface layer of a soap bubble of diameter 5 mm will be
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid then:
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
Two small drops of mercury each of radius R coalesce to form a large single drop. The ratio of the total surface energies before and after the change is
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
When two soap bubbles of radii a and b(b>a) coalesce, the radius of curvature of common surface is:
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
A soap bubble of radius R is blown. After heating the solution, a second bubble of radius 2R is blown. The work required to blow the second bubble in comparison to that required for the first bubble is
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If σ is the surface tension of the soap solution, the energy spent in the process is
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
A small soap bubble of radius 4cm is trapped inside another bubble of radius 6cm without any contact. Let P2 be the pressure inside the inner bubble and P0, the pressure outside the outer bubble. Radius of another bubble with pressure difference P2-P0 between its inside and outside would be:
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Physics>Mechanics>Mechanical Properties of Fluids>Surface Tension
A soap bubble, blown by a mechanical pump at the mouth of a tube increases in volume with time at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by: