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
Advertisements
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
Draw a neat labelled diagram showing forces acting on the meniscus of water in a capillary tube.
The surface tension of water at 0ºc is 75·5 dyne/cm. Find surface tension of water at 25°C. [ α for water = 0·0021/°C ]
Explain why Surface tension of a liquid is independent of the area of the surface
Explain why A drop of liquid under no external forces is always spherical in shape
Figure (a) shows a thin liquid film supporting a small weight = 4.5 × 10–2 N. What is the weight supported by a film of the same liquid at the same temperature in Fig. (b) and (c)? Explain your answer physically.
Mercury has an angle of contact equal to 140° with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside? Surface tension of mercury at the temperature of the experiment is 0.465 N m–1. Density of mercury = 13.6 × 103 kg m–3
Mercury has an angle of contact equal to 140° with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside? Surface tension of mercury at the temperature of the experiment is 0.465 N m–1. Density of mercury = 13.6 × 103 kg m–3
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.
A big drop of radius R is formed from 1000 droplets of water. The radius of a droplet will be _______
A) 10 R
B) R/10
C) R/100
D) R/1000
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?
Frictional force between solids operates even when they do not move with respect to each other. Do we have viscous force acting between two layers even if there is no relative motion?
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 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.
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.
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.
A capillary tube of radius 1 mm is kept vertical with the lower end in water. (a) Find the height of water raised in the capillary. (b) If the length of the capillary tube is half the answer of part , find the angle θ made by the water surface in the capillary with the wall.
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 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.
Solve the previous problem if the lead piece is fastened on the top surface of the block and the block is to float with its upper surface just dipping into water.
A cubical metal block of edge 12 cm floats in mercury with one fifth of the height inside the mercury. Water in it. Find the height of the water column to be poured.
Specific gravity of mercury = 13.6.
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.
Water level is maintained in a cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel.
The energy stored in a soap bubble of diameter 6 cm and T = 0.04 N/m is nearly ______.
Why is the surface tension of paints and lubricating oils kept low?
How much amount of work is done in forming a soap bubble of radius r?
Explain the capillary action.
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 ______
Explain the phenomena of surface tension on the basis of molecular theory.
Obtain an expression for the capillary rise or fall using the forces method.
How does surface tension help a plant?
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
Mention the S.I unit and dimension of surface tension.
How is surface tension related to surface energy?
What do you mean by capillarity or capillary action?
A drop of oil placed on the surface of water spreads out. But a drop of water place on oil contracts to a spherical shape. Why?
What is capillarity?
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?
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 ____________.
Two spherical rain drops reach the surface of the earth with terminal velocities having ratio 16 : 9. The ratio of their surface area is ______.
If the surface tension of a soap solution is 3 × 10-2 N/m then the work done in forming a soap film of 20 cm × 5 cm will be ______.
A molecule of water on the surface experiences a net ______.
The wear and tear in the machine part is due to ______.
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.
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?
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 drop of water and a soap bubble have the same radii. Surface tension of soap solution is half of that of water. The ratio of excess pressure inside the drop and bubble is ______.
When one end of the capillary is dipped in water, the height of water column is 'h'. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of capillary is ______.
(Surface tension of water = 7 × 10-2 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 ______.
Define angle of contact.
