Advertisements
Advertisements
प्रश्न
Eight droplets of water each of radius 0.2 mm coalesce into a single drop. Find the decrease in the surface area.
Advertisements
उत्तर
r = radius of droplet
= 0.2 mm = 2 × 10-4 m
R = radius of single drop
Volume of 8 droplets = Volume of a single drop
`8 xx 4/3 pi "r"^3 = 4/3 pi"R"^3`
∴ R3 = 8r3
∴ R = 2r
Decrease in the surface area
ΔA = A1 - A2
= 8 × 4πr2 - 4πR2
= 32πr2 - 4π(2r)2
= 32πr2 - 16πr2
= 16πr2
= 16 × 3.142 × (2 × 10-4)2
ΔA = 2.011 × 10-6 m2
∴ Decrease in the surface area is 2.011 × 10-6 m2.
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.
Angle of contact for the pair of pure water with clean glass is _______.
Water rises to a height 3.2 cm in a glass capillary tube. Find the height to which the same water will rise in another glass capillary having half area of cross section.
'n' droplets of equal size of radius r coalesce to form a bigger drop of radius R. The energy liberated is equal to...................
(T =Surface tension of water)
`(a) 4piR^2T[n^(1/3)-1]`
`(b) 4pir^2T[n^(1/3)-1]`
`(c) 4piR^2T[n^(2/3)-1]`
`(d)4 pir^2T[n^(2/3)-1]`
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 ]
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
Define surface tension and surface energy.
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
A uniform vertical tube of circular cross section contains a liquid. The contact angle is 90°. Consider a diameter of the tube lying in the surface of the liquid. The surface to the right of this diameter pulls the surface on the left of it. What keeps the surface on the left in equilibrium?
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?
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
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 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 drop of mercury of radius 2 mm is split into 8 identical droplets. Find the increase in surface energy. Surface tension of mercury = 0.465 J m−2.
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.
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?
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 ______.
Explain the capillary action.
Derive an expression for capillary rise for a liquid having a concave meniscus.
A drop of mercury of radius 0.2 cm is broken into 8 droplets of the same size. Find the work done if the surface tension of mercury is 435.5 dyn/cm.
The surface tension of a liquid at critical temperature is ______
Define surface tension.
What will be the shape of the liquid meniscus for the obtuse angle of contact?
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?
Two soap bubbles have a radius in the ratio of 2:3. Compare the works done in blowing these bubbles.
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.
Numerical Problem.
A stone weighs 500 N. Calculate the pressure exerted by it if it makes contact with a surface of area 25 cm2.
Describe an experiment to prove that friction depends on the nature of a surface.
The wettability of a surface by a liquid depends primarily on
Define the surface tension of a liquid.
Define the angle of contact for a given pair of solid and liquid.
Obtain an expression for the excess of pressure inside a
- liquid drop
- liquid bubble
- air bubble
Obtain an expression for the surface tension of a liquid by the capillary rise method.
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 ______
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 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.
In a U-tube, the radii of two columns are respectively r1 and r2. When a liquid of density ρ(θ = 0°) is filled in it, a level difference of h is observed on two arms, then the surface tension of the liquid is ______.
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 ______.
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)
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 ______.
In most liquids, with the rise in temperature, the surface tension of a liquid ______.
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 ______.
Find the work done when a drop of mercury of radius 2 mm breaks into 8 equal droplets. [Surface tension of mercury = 0.4855 J/m2].
A drop of water of radius 8 mm breaks into number of droplets each of radius 1 mm. How many droplets will be formed?
Define angle of contact.
