Advertisements
Advertisements
प्रश्न
A u-tube is made up of capillaries of bore 1 mm and 2 mm respectively. The tube is held vertically and partially filled with a liquid of surface tension 49 dyne/cm and zero angles of contact. Calculate the density of the liquid, if the difference in the levels of the meniscus is 1.25 cm. take g = 980 cm/s2
उत्तर
Let ‘r1’ be the radius of one bore and ‘r2’ be the radius of the second bore of the U-tube. Then, if ‘h1’ and ‘h2’ are the height of water on two sides, then
h1 = `(2T cosθ)/(r_1ρg)` ..........(i)
and h2 = `(2T cosθ)/(r_2ρg)` .................(ii)
Subtracting equation (ii) from equation (i),
h1 - h2 = `(2T cosθ)/(r_1ρg) - (2T cosθ)/(r_2ρg) = (2T cosθ)/(ρg)[1/r_1 - 1/r_2]`
∴ ρ = `(2Tcosθ)/((h_1 - h_2)g)[1/r_1 - 1/r_2]`
Given: T = 49 dyne/cm, θ = 0°,
h1 − h2 = 1.25 cm, g = 980 cm/s2
r1 = `1/2` mm = 0.5 mm = 5 × 10-2 cm
r2 = `2/2` mm = 1 mm = 10-1 cm
∴ ρ = `(2 xx 49 xx cos0^circ)/(1.25 xx 980) xx [1/(5 xx 10^-2) - 1/10^-1]`
= `1/12.5[20 - 10]`
= `10/12.5 = 1/1.25`
Using reciprocal table,
ρ = 0.8 g/cm3
The density of liquid is ρ = 0.8 g/cm3.
APPEARS IN
संबंधित प्रश्न
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 an expression for excess pressure inside a drop of liquid.
A raindrop of diameter 4 mm is about to fall on the ground. Calculate the pressure inside the raindrop. [Surface tension of water T = 0.072 N/m, atmospheric pressure = 1.013 x 105 N/m2 ]
In which of the following substances, surface tension increases with increase in temperature ?
- Copper
- Molten copper
- Iron
- Molten iron
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?
The total energy of free surface of a liquid drop is 2π times the surface tension of the liquid. What is the diameter of the drop? (Assume all terms in SI unit).
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
The contact angle between pure water and pure silver is 90°. If a capillary tube made of silver is dipped at one end in pure water, will the water rise in the capillary?
The force of surface tension acts tangentially to the surface whereas the force due to air pressure acts perpendicularly on the surface. How is then the force due to excess pressure inside a bubble balanced by the force due to the surface tension?
If water in one flask and castor oil in other are violently shaken and kept on a table, which will come to rest earlier?
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
Air is pushed into a soap bubble of radius r to double its radius. If the surface tension of the soap solution in S, the work done in the process is
If more air is pushed in a soap bubble, the pressure in it
If two soap bubbles of different radii are connected by a tube,
Viscosity is a property of
The properties of a surface are different from those of the bulk liquid because the surface molecules
(a) are smaller than other molecules
(b) acquire charge due to collision from air molecules
(c) find different type of molecules in their range of influence
(d) feel a net force in one direction.
A liquid is contained in a vertical tube of semicircular cross section. The contact angle is zero. The force of surface tension on the curved part and on the flat part are in ratio
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 surface energy of water kept in a cylindrical vessel of radius 6.0 cm. Surface tension of water = 0.075 J m−2.
Two large glass plates are placed vertically and parallel to each other inside a tank of water with separation between the plates equal to 1 mm. Find the rise of water in the space between the plates. Surface tension of water = 0.075 Nm−1.
A metal piece of mass 160 g lies in equilibrium inside a glass of water. The piece touches the bottom of the glass at a small number of points. If the density of the metal is 8000 kg/m3, find the normal force exerted by the bottom of the glass on the metal piece.
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 cubical box is to be constructed with iron sheets 1 mm in thickness. What can be the minimum value of the external edge so that the cube does not sink in water? Density of iron = 8000 kg/m3 and density of water = 1000 kg/m3.
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?
Derive an expression for capillary rise for a liquid having a concave meniscus.
The water droplets are spherical in free fall due to ______
Water rises to a height of 20 mm in a capillary tube. If the radius made 1/3rd of its previous value, to what height will the water now rise in the tube?
Explain the phenomena of surface tension on the basis of molecular theory.
The wettability of a surface by a liquid depends primarily on
Mention the S.I unit and dimension of surface tension.
How is surface tension related to surface energy?
Distinguish between cohesive and adhesive forces.
A capillary of diameter d mm is dipped in water such that the water rises to a height of 30 mm. If the radius of the capillary is made `(2/3)` of its previous value, then compute the height up to which water will rise in the new capillary?
The surface tension of the two liquids is respectively 20 and 60 dyne cm-1. The liquids drop from the ends of two tubes of the same radius. The ratio of the weights of the two drops is ______
Water rises upto a height h in a capillary tube on the surface of the earth. The value of h will increase, if the experimental setup is kept in [g = acceleration due to gravity]
The excess of pressure, due to surface tension, on a spherical liquid drop of radius 'R' is proportional to ______.
A large number of liquid drops each of radius 'r' coalesce to form a big drop of radius 'R'. The energy released in the process in converted into kinetic energy of the big drop. The speed of the big drop is ______. (T = surface tension of liquid, p = density of liquid)
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.
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?
Two mercury droplets of radii 0.1 cm. and 0.2 cm. collapse into one single drop. What amount of energy is released? The surface tension of mercury T = 435.5 × 10–3 Nm–1.
If a drop of liquid breaks into smaller droplets, it results in lowering of temperature of the droplets. Let a drop of radius R, break into N small droplets each of radius r. Estimate the drop in temperature.
The sufrace tension and vapour pressure of water at 20°C is 7.28 × 10–2 Nm–1 and 2.33 × 103 Pa, respectively. What is the radius of the smallest spherical water droplet which can form without evaporating at 20°C?
Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of the two limbs, of the tube?
[Take surface tension of water T = 7.3 × 10-2 Nm-1, angle of contact = 0, g = 10 ms-2 and density of water = 1.0 × 103 kgm-3]
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].
Work done to blow a bubble of volume V is W. The work done in blowing a bubble of volume 2V will be ______.
