# Physics Important Questions: Surface Tension

 Maharashtra State Board > Science >  Surface tension > You are Here

### Very Short Answers (1 Mark)

Q1. Define:

a) Cohesive force and Adhesive force:

• The attractive force between the two molecules of the same substance is called as a cohesive force. e.g. attractive force between water and water molecules.
• The attractive force between the two molecules of the different substance is called an adhesive force. e.g. attractive force between water and glass molecules.

b) Range of molecular forces:

• The maximum distance between two molecules up to which the intermolecular forces are effective is called the range of molecular forces.

c) Sphere of influence:

• A sphere drawn by taking the radius equal to the range of molecular attraction and centre as the centre of the molecule is called sphere of molecular influence.

d) Surface tension:

• Surface tension or force of surface tension is the force per unit length of an imaginary line drawn in any direction on the free surface of a liquid, the line of action of the force being on the surface and at right angles to the length of the imaginary line.

e) Angle of contact:

• When the liquid is in contact with solid, the angle between the solid surface and the tangent to the free surface of the liquid at the point of contact, measured from inside the liquid is called the angle of contact.

Q2. What is capillarity?

• The phenomenon of a rise and fall of a liquid inside a capillary tube when it is dipped in the liquid is called capillary action or capillarity.

Q3. What is surface energy?

• Every molecule on the surface and surface film possesses a certain amount of potential energy. This energy is called surface energy.

Q4. Water spiders are able to walk on the surface of the water, why?

• Water spiders are able to walk on the surface of the water because their feet produce dimples on the surface film without rupturing the film.  As soon as a foot is lifted the film which is under tension again becomes flat.
• The feet of spider produce dimples on the surface film without rupturing the film. Due to which the surface tension acts in an inclined manner. The vertical component of the surface tension supports the weight of the insect.
• As soon as a foot is lifted the film which is under tension again becomes flat.

Q5. A steel blade floats on the surface of the pure water when detergent is added it sinks. Why?

• A safety razor blade, when placed gently with its flat surface on water floats on it even though the density of steel, is nearly eight times greater than that of water. The surface film forms due to surface tension support the needle/blade and their thickness is not sufficient to break the film.
• But when the detergent is added to the water the surface tension of water decreases and the thickness of the surface film decreases. Now the thickness of the blade is sufficient to break the surface film and it sinks.

Q6. A small air bubble of radius ‘ r’ in water is at depth ‘h’, below the water surface. If P is atmospheric pressure, ‘d’ is the density of water and T is surface tension of water then what is the pressure inside the bubble?

• As the bubble is below the surface of the liquid, the total pressure on it is atmospheric pressure (P) plus pressure due to liquid column (hdg) and excess of pressure outside the bubble (2T/r).
• This pressure is balanced by the pressure inside the bubble.

Hense the pressure inside bubble = P + hdg +2T/r

Q7. Arun says that molecular forces do not obey the inverse square law of distance. Ashok says that molecular forces obey the inverse square law of distance. State your opinion.

• Arun is correct because molecular forces do not obey the inverse square law of distance

Q8. What is the nature of the molecular forces?

• These are short range forces may be of attraction or repulsion. They do not obey the inverse square law.

Q9. What is the effect of temperature on the angle of contact?

• The angle of contact increases with the increase in temperature of the liquid.

Q10. “Tents are coated with a thin layer of aluminum hydroxide”, why?

• Tent cloths are woven in such a way that the water particles do not penetrate through it. But the clothes are able to stop the water drops coming down with high speed (like rain).
• Aluminium hydroxide is insoluble in water and acts as a very good water repellant. So it drains off the water from the tent material preventing it from wetting the cloth.

Q11. “The threads of raincoat are coated with waterproofing agents like resin”, why?

• The material of raincoat is woven in such a way that the water particles do not penetrate through it.
• The resin is insoluble in water and acts as a very good water repellant. So it drains off the water from the outer surface of the raincoat preventing it from wetting from inside.

### Short Answers I (2 Marks)

Q1. Show that surface tension is numerically equal to surface energy per unit area.

• Consider a rectangular frame ABCD in which side CD is made of loose write and other three sides are fixed. The frame is immersed in a soap solution and taken out and held horizontally. A film of soap solution will be formed on the frame and it will at once try to shrink and pull the loose wire CD towards AB. If the length of loose wire CD is  ‘l’ and the film is of finite thickness, therefore the film will be in contact with the wire both on the upper surface as well as along its lower surface.  Hence the length of the wire in contact with the film is ‘ 2l ‘.  The force acting on the wire is directed towards AB, per unit length of the contact line is surface tension (T). By definition of surface tension, we have

T = F / 2l

∴    F  =  T . 2 l     …  (1)

• Imagine an external force is applied on CD which is equal and opposite to force F Let the wire at CD moves to C’D’ through small distance dx.  Then the work done against the force of surface tension is given by

dW  =  F.dx         …  (2)

From equations (1) and (2),

dW = T.2l. dx

But,  2l . dx = dA = increase in Area of both the surface of the film.

∴  dW   =  T.dA

This work done is stored inside the films as potential energy dU.

∴   dU  =  T.dA

• If, initially CD is very close to AB, initial energy and initial area of the film can be taken as zero and dU and dA can be treated as total energy and the total area of the film respectively.

∴  T  =  dU / dA

• This expression indicates that surface tension is equal to surface energy per unit area of the surface film.

Q2. Obtain the dimensions of surface tension. State its SI unit.

Dimensions of Surface tension:

Surface Tension (T)  = Force (F) / Effective Length (L)

∴   [T] = [F] / [L]

∴   [T] = [L1M1T-2] / [L1]

∴   [T] = [L0M1T-2]

Thus the dimensions of surface tension are [L0M1T-2].

S.I. Unit of Surface Tension:

S.I. unit of surface tension is  newton per metre (N m-1)

Q3. State any four applications of capillarity.

• Due to capillary action oil rises through the wicks of lamps.
• Due to capillary action water rises through sap of trees.
• Due to capillary action ink is absorbed by blotting paper.
• Due to capillary action liquids are absorbed by sponges.
• Bricks and mortar, which are porous, permit the rise of soil water through them by capillary action. To avoid it base is made using damp-proof cement.
• Soil water rises to the surface by capillary action and evaporates. To conserve soil water, the farmers plough their fields in summer. The loosening of the top layer of the soil breaks up the fine capillaries through which the deeper down water is sucked up. Thus the loss of water in the soil is prevented.
• Due to depression in the level of mercury in a capillary tube, a correction is to be applied for mercury barometer.

Q4. State the characteristics of the angle of contact.

• The angle of contact is constant for a given liquid-solid pair.
• When the angle of contact between the liquid and a solid surface is small (acute), the liquid is said to wet the surface. Thus water wets glass.
• If the angle of contact is large the surface is not wetted. Mercury does not wet glass.
• If there are impurities in liquid, then they alter the values of angle of contact.
• The angle of contact decreases with increase in temperature.
• For a liquid which completely wets the solid, the angle of contact is equal to zero.

Q5. The radii of two columns r1 and r2 when a liquid of density ρ, the angle of contact (θ = 0°) is filled in it. The level difference of liquid in two arms is ‘h’. Find the surface tension.

Since θ = 0o cos θ = 1. We assume r2 > r1 hence h1 > h22

Rise of liquid in the capillary tube is given by h=2T/(rρg)

For tube of radius r1 We have, h1 = 2T/(r1ρg)

For tube of radius r2 We have, h2 = 2T/(r2ρg)

The level difference of liquid in the two arms is given by

This is the expression for surface tension

Q6. Why do molecules of a liquid lying in the surface film possess extra energy?

• The molecules on the surface and in a surface film of thickness equal to the range of molecular attraction of the liquid molecule experience a net force in the downward direction.  The magnitude of force depends upon the distance of the molecule from the free surface.
• The behaviour of this film is different from that of the rest of the liquid.  It is called the surface film.  If any molecule is brought to the surface from the liquid, the work is to be done against this net downward force. This work increases the potential energy of the surface. Hence the molecules of a liquid lying in the surface film possess extra energy.

Q7. Draw a neat labelled diagram to show the angle of contact between  (a) pure water and clean glass (b) mercury and clean glass

### Short Answers II (3 Marks):

Q1. Define angle of contact. Explain why it is acute in case of water

• When the liquid is in contact with solid, the angle between the solid surface and the tangent to the free surface of the liquid at the point of contact, measured from inside the liquid is called the angle of contact.
• When impure water or kerosene is taken in a glass vessel, it is found that the surface near the walls is curved concave upwards.

• Consider a molecule of water M on the free surface very close to the wall of the glass vessel. The force of cohesion C due to other water molecules is as shown in the figure. In addition to this, a force of adhesion A acts due to the glass molecule as shown in the figure. The net adhesive force between water molecules and air molecules is negligible. The gravitational force on the molecule is also negligible.
• The magnitude of A is greater than the magnitude of C and resultant of the two molecular forces of attraction R is directed towards the glass or outside the liquid. Hence the molecule A is attracted towards the walls of glass vessel.
• The free surface of water adjusts itself at right angles to the resultant R. Therefore molecules like M creep upward on the solid surface. Thus the water surface is curved concave upwards and the angle of contact is acute.

Q2. Define angle of contact . Explain why it is obtuse in case of liquids which do not wet solids.

• When the liquid is in contact with solid, the angle between the solid surface and the tangent to the free surface of the liquid at the point of contact, measured from inside the liquid is called the angle of contact.
• When mercury is taken in a glass vessel, it is found that the surface near the walls is curved convex upwards.

• Consider a molecule of mercury M on the free surface very close to the wall of the glass vessel. The force of cohesion C  due to other mercury molecules is as shown in the figure. In addition to this, a force of adhesion A acts due to the glass molecule as shown in the figure. The net adhesive force between mercury molecules and air molecules is negligible. The gravitational force on the molecule is also negligible.
• The magnitude of  A is very less than the magnitude of C and resultant of the two molecular forces of attraction R is directed inside the liquid. Hence the molecule A is attracted towards other molecules of mercury.
• The free surface adjusts itself at right angles to the resultant R. The molecule A creeps downwards on the glass surface. Thus the surface of the mercury in the glass is curved convex upwards and the angle of contact is obtuse.

Q3. Explain the formation of the concave and convex surface of liquid on the basis of molecular theory.

Formation of Concave Surface:

• When impure water or kerosene is taken in a glass vessel, it is found that the surface near the walls is curved concave upwards.

• Consider a molecule of water M on the free surface very close to the wall of the glass vessel. The force of cohesion C due to other water molecules is as shown in the figure. In addition to this, a force of adhesion A acts due to the glass molecule as shown in the figure. The net adhesive force between water molecules and air molecules is negligible. The gravitational force on the molecule is also negligible.
• The magnitude of A is greater than the magnitude of C and resultant of the two molecular forces of attraction R is directed towards the glass or outside the liquid. Hence the molecule A is attracted towards the walls of glass vessel.
• The free surface of water adjusts itself at right angles to the resultant R. Therefore molecules like M creep upward on the solid surface. Thus the water surface is curved concave upwards and the angle of contact is acute.

Formation of Convex Surface:

• When the liquid is in contact with solid, the angle between the solid surface and the tangent to the free surface of the liquid at the point of contact, measured from inside the liquid is called the angle of contact.
• When mercury is taken in a glass vessel, it is found that the surface near the walls is curved convex upwards.

• Consider a molecule of mercury M on the free surface very close to the wall of the glass vessel. The force of cohesion C  due to other mercury molecules is as shown in the figure. In addition to this, a force of adhesion A acts due to the glass molecule as shown in the figure. The net adhesive force between mercury molecules and air molecules is negligible. The gravitational force on the molecule is also negligible.
• The magnitude of  A is very less than the magnitude of C and resultant of the two molecular forces of attraction R is directed inside the liquid. Hence the molecule A is attracted towards other molecules of mercury.
• The free surface adjusts itself at right angles to the resultant R. The molecule A creeps downwards on the glass surface. Thus the surface of the mercury in the glass is curved convex upwards and the angle of contact is obtuse.

Q4. Obtain the relation between surface tension and surface energy.

• Consider a rectangular frame ABCD in which side CD is made of loose write and the other three sides are fixed. The frame is immersed in a soap solution and taken out and held horizontally. A film of soap solution will be formed on the frame and it will at once try to shrink and pull the loose wire CD towards AB. If the length of loose wire CD is  ‘l’ and the film is of finite thickness, therefore the film will be in contact with the wire both on the upper surface as well as along its lower surface.  Hence the length of the wire in contact with the film is ‘ 2l ‘.  The force acting on the wire is directed towards AB, per unit length of the contact line is surface tension (T). By definition of surface tension, we have

T = F / 2l

∴    F  =  T . 2 l     …  (1)

• Imagine an external force is applied on CD which is equal and opposite to force F Let the wire at CD moves to C’D’ through small distance dx.  Then the work done against the force of surface tension is given by

dW  =  F.dx         …  (2)

From equations (1) and (2),

dW = T.2l. dx

But,  2l . dx = dA = increase in Area of both the surface of the film.

∴  dW   =  T.dA

This work done is stored inside the films as potential energy dU.

∴   dU  =  T.dA

• If, initially CD is very close to AB, initial energy and initial area of the film can be taken as zero and dU and dA can be treated as total energy and the total area of the film respectively.

∴  T  =  dU / dA

• This expression indicates that surface tension is equal to surface energy per unit area of the surface film.

Q5. Derive Laplace’s law for spherical membrane .

• Due to the spherical shape, the inside pressure Pis always greater than the outside pressure Po. The excess of pressure is Pi– Po.

• Let the radius of the drop increases from r to r + Δr, where Δr is very very small, hence the inside pressure is assumed to be constant.

Initial surface area = A = 4 π r²

Final surface area = A = 4 π (r + Δr)² = 4 π (r² + 2r.Δr + Δr²) =  4 πr² + 8 πr.Δr + 4 πΔr²

Δr is very very small, hence Δr² still smsll hence the term 4 πΔr² can be neglected.

Final surface area = A =  4 πr² + 8 πr.Δr

Hence Change in area = A – A =  4 πr² + 8 πr.Δr  –  4 πr²

Change in area = dA =  8 πr.Δr

Now, work done in increasing the surface area is given by

dW = T. dA = T.  8 πr.Δr    …………… (1)

By definition of work in mechanics we have

dW = Force ∴ displacement = F .Δr  …………… (2)

But P = F /A, Hence F = Excess pressure × Area

F = (Pi– Po) × 4 πr²

Substituting in equation (2) we have

dW = (Pi– Po) × 4 πr².Δr  …………… (3)

From equations (3) and (4) we have

(Pi– Po) × 4 πr².Δr  = T.  8 πr.Δr

(Pi– Po) = 2T / r

This relation is known as Laplace’s law for the spherical membrane for a liquid drop.

For bubble there are two free surfaces, Hence the Laplace’s law for bubble can be written as

(Pi– Po) = 4T / r

Q6. Describe the capillary tube experiment to determine the height of the water rise in the capillary tube. Hence find the surface tension of water. [Given: radius of the capillary is ‘r’ and angle of contact is θ = 0°]

• A glass capillary tube is dipped in a beaker containing water whose surface tension is to be measured. Due to surface tension, the water level rises up inside the capillary. The phenomenon is known as capillary action or capillarity.
• Using a travelling microscope, the microscope is focused on the lower meniscus of the curved concave surface. The reading is taken using the microscope. The microscope is lowered and it is focused on the water level inside the beaker. The reading is taken again.
• The difference between the two readings gives the height of the water column inside capillary (h).
• The inner diameter of the capillary tube is measured using the travelling microscope. Hence we calculate the radius of the bore (r).(Given in this case)
• Using the following formula Surface tension (T) can be calculated.

where, ρ =  Density of liquid

g  =  Acceleration due to gravity

θ =  Angle of contract (given 0°)

cos θ = cos0°  = 1

Hence the formula for the surface tension of water reduces to

h = 2T / (rρg)

Q7. Describe the capillary tube experiment to determine the surface tension of a liquid.

• A glass capillary tube is dipped in a beaker containing liquid whose surface tension is to be measured. Due to surface tension, the liquid level rises up inside the capillary. The phenomenon is known as capillary action or capillarity.
• Using a travelling microscope, the microscope is focused on the lower meniscus of the curved concave surface. The reading is taken using the microscope. The microscope is lowered and it is focused on the liquid level inside the beaker. The reading is taken again.
• The difference between the two readings gives the height of the liquid column inside capillary (h).
• The inner diameter of the capillary tube is measured using the travelling microscope. Hence we calculate the radius of the bore (r).
• Using the following formula Surface tension (T) can be calculated.

T = (hrρg) / 2cosθ

where, ρ =  Density of liquid

g  =  Acceleration due to gravity

θ =  Angle of contract

Q8. Explain the surface tension on the basis of molecular theory.

• Consider three molecules A, B and C in a liquid, such that molecule A is well inside the liquid, molecule B is close to the free surface and the molecule C is on the free surface.
• The sphere of influence of the molecule A is completely inside the liquid, and hence it will be acted upon by equal forces in all directions and these forces will balance one another and the net force acting on it is zero.
• For molecule B, a part of the upper half of the sphere of influence is in the air, which contains air molecules.  Air molecules exert very negligible adhesive forces on molecule B.  Therefore, the cohesive forces due to molecules in the liquid remains unbalanced and thus a net force in downward direction acts on the molecule.
• For molecule C, the upper half of the sphere of influence is completely in the air. Due to this, the force of attraction due to the molecules inside the lower half of the sphere will remain unbalanced.  This molecule experiences the maximum possible unbalanced force in the downward direction.
• Thus the molecules on the surface and in a surface film of thickness equal to the range of molecular attraction of the liquid molecule experience a net force in the downward direction.  The magnitude of force depends upon the distance of the molecule from the free surface.  The behaviour of this film is different from that of the rest of the liquid.  It is called the surface film.  This film behaves like a film which is under tension.  This phenomenon is known as surface tension.
• If any molecule is brought to the surface from the liquid, the work is to be done against this net downward force. This work increases the potential energy of the surface. But the liquid surface will have the tendency to have minimum potential energy. So a minimum number of molecules remains on the surface of the liquid.
• Thus the free surface of a liquid behaves like a stretched elastic membrane and has a tendency to contract so as to minimize its surface area.

Q9. Obtain an expression, for the rise of a liquid in a capillary tube.

• If a glass tube of a smaller bore (capillary tube) is immersed in a liquid which wets the glass (water), then the liquid level inside the tube rises. If the tube is immersed in a liquid which does not wet the glass (mercury), then the liquid level inside the tube decreases. This phenomenon of the rise or fall of liquid in a capillary tube is called capillary action or capillarity.
• Consider a capillary tube immersed in a liquid that wets it. The liquid will rise in the capillary tube. The surface of the liquid will be concave.

• The surface tension ‘T’ acts along the tangent to the liquid surface at the point of contact as shown. Let θ be the angle of contact. The force of surface tension is resolved into two components vertical T cos θ and horizontal T sin θ. The components T sinθ cancel each other as they are equal in magnitude and radially outward (opposite to each other). The unbalanced component T cos θ will push the liquid up into the capillary tube. This explains the rise in the liquid layer in the capillary tube.
1. If ‘r’ is the radius of the bore of the capillary tube, the length along which the force of surface tension acts is 2πr. Hence total upward force is  2πr T cos θ.
2. Due to this force the liquid rise up in the tube. The weight of liquid acts vertically downward. The liquid goes on rising till the force of surface tension is balanced by the weight of the liquid column.

Total upward force  =  Weight of liquid in the capillary tube.

2πr T cos θ  =    mg

Where ‘m’ is the mass of liquid in the capillary tube.

2πr T cos θ   =    V ρ g

Where ‘V’ is the volume of liquid in capillary and ρ is the density of the liquid in the capillary tube.

2πr T cos θ   =    π r²h ρ g

Where ‘h’ is the height of the liquid column in the capillary tube. then

This is an expression for the rise in the liquid in the capillary tube.

Q10. Why there is a rise of liquid inside the capillary tube?

• If a glass tube of a smaller bore (capillary tube) is immersed in a liquid which wets the glass (water), then the liquid level inside the tube rises. If the tube is immersed in a liquid which does not wet the glass (mercury), then the liquid level inside the tube decreases. This phenomenon of the rise or fall of liquid in a capillary tube is called capillary action or capillarity.
• Consider a capillary tube immersed in a liquid that wets it. The liquid will rise in the capillary tube. The surface of the liquid will be concave.

• The surface tension ‘T’ acts along the tangent to the liquid surface at the point of contact as shown. Let θ be the angle of contact. The force of surface tension is resolved into two components vertical T cos θ and horizontal T sin θ. The components T sinθ cancel each other as they are equal in magnitude and radially outward (opposite to each other). The unbalanced component T cos θ will push the liquid up into the capillary tube. This explains the rise in the liquid layer in the capillary tube.
• If ‘r’ is the radius of the bore of the capillary tube, the length along which the force of surface tension acts is 2πr. Hence total upward force is  2πr T cos θ.
• Due to this force the liquid rise up in the tube. The weight of liquid acts vertically downward. The liquid goes on rising till the force of surface tension is balanced by the weight of the liquid column.
• The height of liquid colum in capillary tube is given by

where h  =  height of liquid level in capillary

T  =  Surface tension

ρ =  Density of liquid

r  =  Radius of the bore of the capillary tube

g  =  Acceleration due to gravity

θ =  Angle of contract

Q11. Draw diagram showing force due to surface tension at the liquid-solid, air –solid, air-liquid interface, in case of (a) drop of mercury on a plane solid surface and b) drop of water on a plane solid surface. Discuss the variation of the angle of contact.

For equilibrium of the drop

T2 = T1 + T3 cos θ

a) drop of mercury on a plane solid surface

If T2 < T1, and T1 -T2 < T3, then cos θ is negative and the angle of contact is obtuse.

Mercury does not wet the glass and thus it forms a drop on the glass.

b) drop of water on a plane solid surface

T2 > T1, and T2 -T1 < T3, then cos θ  is positive and the angle of contact is acute.

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