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 - Physics


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)



Diameter of the first bore, d1 = 3.0 mm = 3 × 10–3 m

Hence the radius of the first bore, `r_1 = d_1/2 = 1.5 xx 10^(-3) m`

Diameter of the second bore, `d_2`= 6.0 mm

Hence the radius of the second bore, `r_2 = d_2/2 = 3xx 10^(-3) m`

Surface tension of water `s = 7.3 xx 10^(-2) Nm^(-1)`

Angle of contact between the bore surface and water, θ= 0

Density of water, ρ =1.0 × 103 kg/m–3

Acceleration due to gravity, g = 9.8 m/s2

Let h1 and hbe the heights to which water rises in the first and second tubes respectively. These heights are given by the relations:

`h_1 = (2s cos theta)/(r_1rhog)`   ...(i)

`h_2 = (2scos theta)/(r_2rhog)` ...(ii)

The difference between the levels of water in the two limbs of the tube can be calculated as:

`= (2 s cos theta)/(r_1rhog) - (2 s cos theta)/(r_2rhog)`

`= (2 s cos theta)/(rhog)[1/r_1 - 1/r_2]`

`= (2xx 7.3 xx 10^(-2) xx 1)/(1xx10^3xx9.8) [1/(1.5xx10^(-3)) - 1/(3xx10^(-3))]`

`= 4.966 xx 10^(-3) m`

= 4.97 mm

Hence, the difference between levels of water in the two bores is 4.97 mm.

Concept: Surface Tension
  Is there an error in this question or solution?
Chapter 10: Mechanical Properties of Fluids - Exercises [Page 271]


NCERT Physics Class 11
Chapter 10 Mechanical Properties of Fluids
Exercises | Q 30 | Page 271

Video TutorialsVIEW ALL [1]


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)

Derive an expression for excess pressure inside a drop of liquid.

Angle of contact for the pair of pure water with clean glass is _______.

Define the angle of contact.

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.

In which of the following substances, surface tension increases with increase in temperature ?

  1. Copper
  2. Molten copper
  3. Iron
  4. Molten iron

'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 ]

Explain why The angle of contact of mercury with glass is obtuse, while that of water with glass is acute

Explain why A drop of liquid under no external forces is always spherical in shape

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 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?

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

Calculate the work done in increasing the radius of a soap bubble in air from 1 cm to 2 cm. The surface tension of soap solution is 30 dyne/cm. (Π = 3.142).

When a sparingly soluble substance like alcohol is dissolved in water, surface tension of water

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?

It is said that a liquid rises or is depressed in capillary due to the surface tension. If a liquid neither rises nor depresses in a capillary, can we conclude that the surface tension of the liquid is zero?

When the size of a soap bubble is increased by pushing more air in it, the surface area increases. Does it mean that the average separation between the surface molecules is increased?


Water near the bed of a deep river is quiet while that near the surface flows. Give reasons.

A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break

When water droplets merge to form a bigger drop

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be

Viscosity is a property of

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.

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.

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 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. 

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.

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?

Explain the capillary action.

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.

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.

Insect moves over the surface of water because of ______ 

The water droplets are spherical in free fall due to ______ 

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?  

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.  

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/s 

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 the friction arise between the surfaces of two bodies in relative motion?

How does surface tension help a plant?

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

Explain elasticity using intermolecular forces.

Define the surface tension of a liquid.

Mention the S.I unit and dimension of surface tension.

Define the angle of contact for a given pair of solid and liquid.

What are the factors affecting the surface tension of a liquid?

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?

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?

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?

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 ______

A square frame of each side L is dipped in a soap solution and taken out. The force acting on the film formed is _____.
(T = surface tension of soap solution).

Two spherical rain drops reach the surface of the earth with terminal velocities having ratio 16 : 9. The ratio of their surface area is ______.

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

Under isothermal conditions, two soap bubbles of radii 'r1' and 'r2' coalesce to form a big drop. The radius of the big drop is ______.

Soap solution is used for cleaning dirty clothes because ______.

The wear and tear in the machine part is due to ______.

What is surface tension? Explain the applications of surface tension.

Why is raindrop spherical in nature?

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). 

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.

This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.

Eight droplets of water each of radius 0.2 mm coalesce into a single drop. Find the decrease in the surface area.

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 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 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 ______.

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):

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 ______.

When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes `(5r)/4`. Taking the atmospheric pressure to be equal to the 10 m height of the water column, the depth of the lake would approximately be ______.

(ignore the surface tension and the effect of temperature)

The excess pressure inside a liquid drop is 500 Nm-2. If the radius of the drop is 2 mm, the surface tension of the liquid is x × 10-3 Nm-1. The value of x 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)

A liquid drop of density ρ is floating half immersed in a liquid of density d. The diameter of the liquid drop is ______.

(ρ > d, g = acceleration due to gravity, T = surface tension)

In most liquids, with the rise in temperature, the surface tension of a liquid ______.

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].

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.

The surface tension of boiling water is ______.

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.


      Forgot password?
Use app×