Advertisements
Advertisements
प्रश्न
The energy stored in a soap bubble of diameter 6 cm and T = 0.04 N/m is nearly ______.
विकल्प
0.9 × 10–3J
0.4 × 10–3J
0.7 × 10–3J
0.5 × 10–3J
Advertisements
उत्तर
The energy stored in a soap bubble of diameter 6 cm and T = 0.04 N/m is nearly 0.9 × 10–3J
Explanation:
Increase in surface area of the sphere is given by:
A = `4pir^2` ......(i)
Here, r is the radius of the sphere and A is the increase in the surface area.
The bubble contains two surfaces. So multiply Equation (i) by 2
A = `2 xx 4pir^2` .....(ii)
Diameter = 6 cm i.e. r = 3 cm
Substitute the value of r = 3 cm to find the value of the area.
A = `2 xx 4pi xx (3 " cm" xx (1" m")/(100 " cm"))^2`
A = 0.023 m2
The formula for stored energy is:
E = T × A
Here, T is the surface tension.
Substitute the value of T = 0.04 N/m and A = 0.023 m2 to find the stored energy.
E = T × A
E = 0.04 N/m × 0.023 m2
E = 0.9 × 10–3J
APPEARS IN
संबंधित प्रश्न
Derive Laplace’s law for spherical membrane of bubble due to surface tension.
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 ]
Draw a neat labelled diagram showing forces acting on the meniscus of water in a capillary tube.
In which of the following substances, surface tension increases with increase in temperature ?
- Copper
- Molten copper
- Iron
- Molten iron
Explain why Surface tension of a liquid is independent of the area of the surface
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
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)
In a conical pendulum, a string of length 120 cm is fixed at rigid support and carries a mass
of 150 g at its free end. If the mass is revolved in a horizontal circle of radius 0.2 m around a
vertical axis, calculate tension in the string (g = 9.8 m/s2)
Show that the surface tension of a liquid is numerically equal to the surface energy per unit
area.
An ice cube is suspended in vacuum in a gravity free hall. As the ice melts it
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 two soap bubbles of different radii are connected by a tube,
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.
The rise of a liquid in a capillary tube depends on
(a) the material
(b) the length
(c) the outer radius
(d) the inner radius of the tube
When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary.
(a) The surface tension of the liquid must be zero.
(b) The contact angle must be 90°.
(c) The surface tension may be zero.
(d) The contact angle may be 90°.
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.
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.
The lower end of a capillary tube is immersed in mercury. The level of mercury in the tube is found to be 2 cm below the outer level. If the same tube is immersed in water, up to what height will the water rise in the capillary?
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.
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.
Explain the capillary action.
Derive an expression for capillary rise for a liquid having a concave meniscus.
The water droplets are spherical in free fall due to ______
Define surface tension.
The property of _______ of a liquid surface enables the water droplets to move upward in plants.
Numerical Problem.
A stone weighs 500 N. Calculate the pressure exerted by it if it makes contact with a surface of area 25 cm2.
How does surface tension help a plant?
How is surface tension related to surface energy?
Define the angle of contact for a given pair of solid and liquid.
What are the factors affecting the surface tension of a liquid?
What do you mean by capillarity or capillary action?
Obtain an expression for the excess of pressure inside a
- liquid drop
- liquid bubble
- air bubble
What is capillarity?
A spherical soap bubble A of radius 2 cm is formed inside another bubble B of radius 4 cm. Show that the radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is lesser than the radius of both soap bubbles A and B.
Why coffee runs up into a sugar lump (a small cube of sugar) when one corner of the sugar lump is held in the liquid?
Water rises in a capillary tube of radius r upto a height h. The mass of water in a capillary is m. The mass of water that will rise in a capillary of radius `"r"/4` will be ______.
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)
Under isothermal conditions, two soap bubbles of radii 'r1' and 'r2' coalesce to form a big drop. The radius of the big drop is ______.
Why is raindrop spherical in nature?
The angle of contact at the interface of water-glass is 0°, Ethylalcohol-glass is 0°, Mercury-glass is 140° and Methyliodide-glass is 30°. A glass capillary is put in a trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is ______.
Is surface tension a vector?
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 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 ______.
Calculate (i) the pressure due to the weight of the water at a depth of 2.5 m and (ii) the depth below the surface of water at which the pressure due to the weight of the water equals 1.0 atm.
