Advertisements
Advertisements
Question
The total free surface energy of a liquid drop is `pisqrt2` times the surface tension of the liquid. Calculate the diameter of the drop in S.l. unit.
Advertisements
Solution
Given: E = `pi sqrt2` T
To find: Diameter of drop (d)
Formula: E = TΔA
Calculation: ΔA = `4pir^2`
From formula,
E = `4pir^2`T
r = 0.5946 m
∴ d = 2r
= 2(0.5946)
∴ d = 1.1892 m
Diameter of the drop is 1.1892 m.
APPEARS IN
RELATED QUESTIONS
The energy of the free surface of a liquid drop is 5π times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system.
Derive Laplace’s law for spherical membrane of bubble due to surface tension.
The surface tension of water at 0°C is 75.5 dyne/cm. Calculate surface tension of water at 25°C.
(α for water = 2.7×10-3/°C)
Angle of contact for the pair of pure water with clean glass is _______.
Draw a neat labelled diagram showing forces acting on the meniscus of water in a capillary tube.
Explain why Water with detergent dissolved in it should have small angles of contact.
A U-shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 × 10–2 N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film?
What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature (20 °C) is 2.50 × 10–2 N m–1? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1 atmospheric pressure is 1.01 × 105 Pa).
Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is 7.3 × 10–2 N m–1. Take the angle of contact to be zero and density of water to be 1.0 × 103 kg m–3 (g = 9.8 m s–2)
Define surface tension and surface energy.
A body weighs 4.0 kg-wt on the surface of the Earth. What will be its weight on the surface of a plant whose mass is `1/8` th of the mass of the Earth and radius half `(1/2)` of that of the Earth?
State any two characteristics of the angle of contact
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
An ice cube is suspended in vacuum in a gravity free hall. As the ice melts it
When water droplets merge to form a bigger drop
If more air is pushed in a soap bubble, the pressure in it
Which of the following graphs may represent the relation between the capillary rise hand the radius r of the capillary?
Water rises in a vertical capillary tube up to a length of 10 cm. If the tube is inclined at 45°, the length of water risen in the tube will be
A 5.0 cm long straight piece of thread is kept on the surface of water. Find the force with which the surface on one side of the thread pulls it. Surface tension of water = 0.076 N m−1.
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 0.465 N m−1, 0.03 N m−1 and 0.076 N m−1 respectively.
Consider a small surface area of 1 mm2 at the top of a mercury drop of radius 4.0 mm. Find the force exerted on this area (a) by the air above it (b) by the mercury below it and (c) by the mercury surface in contact with it. Atmospheric pressure = 1.0 × 105 Pa and surface tension of mercury = 0.465 N m−1. Neglect the effect of gravity. Assume all numbers to be exact.
The capillaries shown in figure have inner radii 0.5 mm, 1.0 mm and 1.5 mm respectively. The liquid in the beaker is water. Find the heights of water level in the capillaries. The surface tension of water is 7.5 × 10−2 N m−1.
A capillary tube of radius 0.50 mm is dipped vertically in a pot of water. Find the difference between the pressure of the water in the tube 5.0 cm below the surface and the atmospheric pressure. Surface tension of water = 0.075 N m−1.
Consider an ice cube of edge 1.0 cm kept in a gravity-free hall. Find the surface area of the water when the ice melts. Neglect the difference in densities of ice and water.
Find the force exerted by the water on a 2 m2 plane surface of a large stone placed at the bottom of a sea 500 m deep. Does the force depend on the orientation of the surface?
A ferry boat has internal volume 1 m3 and weight 50 kg.(a) Neglecting the thickness of the wood, find the fraction of the volume of the boat immersed in water.(b) If a leak develops in the bottom and water starts coming in, what fraction of the boat's volume will be filled with water before water starts coming in from the sides?
A cubical block of ice floating in water has to support a metal piece weighing 0.5 kg. Water can be the minimum edge of the block so that it does not sink in water? Specific gravity of ice = 0.9.
A cube of ice floats partly in water and partly in K.oil (in the following figure). Find the ratio of the volume of ice immersed in water to that in K.oil. Specific gravity of K.oil is 0.8 and that of ice is 0.9.
A hollow spherical body of inner and outer radii 6 cm and 8 cm respectively floats half-submerged in water. Find the density of the material of the sphere.
A solid sphere of radius 5 cm floats in water. If a maximum load of 0.1 kg can be put on it without wetting the load, find the specific gravity of the material of the sphere.
How much amount of work is done in forming a soap bubble of radius r?
Calculate the rise of water inside a clean glass capillary tube of radius 0.1 mm, when immersed in water of surface tension 7 × 10-2 N/m. The angle of contact between water and glass is zero, the density of water = 1000 kg/m3, g = 9.8 m/s2.
Twenty-seven droplets of water, each of radius 0.1 mm coalesce into a single drop. Find the change in surface energy. Surface tension of water is 0.072 N/m.
The surface tension of a liquid at critical temperature is ______
Describe an experiment to prove that friction depends on the nature of a surface.
The excess of pressure, due to surface tension, on a spherical liquid drop of radius 'R' is proportional to ______.
A molecule of water on the surface experiences a net ______.
A water drop of radius R' splits into 'n' smaller drops, each of radius 'r'. The work done in the process is ______.
T = surface tension of water
The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of the water column and 'h' is the height of water in the capillary. The inner circumference of the capillary is ______.
(surface tension of water = 7 × 10-2 N/m)
Under isothermal conditions, two soap bubbles of radii 'r1' and 'r2' coalesce to form a big drop. The radius of the big drop is ______.
What is surface tension? Explain the applications of surface tension.
The length of a needle floating on water is 2 cm. The additional force due to surface tension required to pull the needle out of water will be (S.T. of water = 7.0 × 10−2 N/m).
For a surface molecule ______.
- the net force on it is zero.
- there is a net downward force.
- the potential energy is less than that of a molecule inside.
- the potential energy is more than that of a molecule inside.
Is surface tension a vector?
The free surface of oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle θ. If the acceleration is a ms–2, what will be the slope of the free surface?
A soap bubble of radius 3 cm is formed inside another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ______ cm.
We have three identical perfectly black plates. The temperatures of first and third plate is T and 3T. What is the temperature of second plate if system is in equilibrium?
A liquid flows out drop by drop from a vessel through a vertical tube with an internal diameter of 2 mm, then the total number of drops that flows out during 10 grams of the liquid flow out ______. [Assume that the diameter of the neck of a drop at the moment it breaks away is equal to the internal diameter of tube and surface tension is 0.02 N/m].
A coaxial cylinder made of glass is immersed in liquid of surface tension ' S'. Radius of inner and outer surface of cylinder are R1 and R2 respectively. Height till which liquid will rise is (Density of liquid is p):
A soap film of surface tension 3 × 10-2 formed in a rectangular frame can support a straw as shown in Fig. If g = 10 ms-12, the mass of the straw is ______.
Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pully as shown in the figure. The system is then released. If M = 2m, then the stress produced in the wire is ______.
The surface tension of soap solution is 25 × 10-3 Nm-1. The excess of pressure inside a soap bubble of diameter 1 cm is ______.
A spherical liquid drop of radius R is divided into eight equal droplets. If surface tension is T, then the work done in this process will be ______.
