Capillarity MCQ Quiz - Objective Question with Answer for Capillarity - Download Free PDF

Solution:

We can use the capillary rise formula to find the radius of the capillary tube:

h = (2T cos θ) / (rρg)

Where:

• h = height of water rise = 7.5 cm = 0.075 m
• T = surface tension of water = 7.5 × 10^-2 N/m
• θ = angle of contact = 0°
• ρ = density of water ≈ 1000 kg/m³
• g = acceleration due to gravity = 10 m/s²
• r = radius of the capillary tube (what we need to find)

Now, rearrange the formula to solve for r:

r = (2T cos θ) / (hρg)

Substituting the given values:

r = (2 × 7.5 × 10^-2 × cos 0°) / (0.075 × 1000 × 10)

r = (2 × 7.5 × 10^-2) / (0.075 × 10000)

r = 0.15 / 750

r = 0.0002 m = 0.2 mm

Hence, the radius of the capillary tube is 0.2 mm (Option 4).

CONCEPT:

Capillary Action and Contact Angle

• When a liquid rises or falls in a narrow tube due to the adhesive forces between the liquid and the tube wall and the cohesive forces within the liquid, it is known as capillary action.
• The angle of contact (θ) is the angle formed between the tangent to the liquid surface and the solid surface inside the tube.
• Water typically has a low contact angle with materials it can wet (hydrophilic materials), leading to capillary rise.
• If the tube is made hydrophobic (e.g., by coating with wax), the contact angle increases, leading to a decrease in the height of the liquid rise.

EXPLANATION:

• Let's examine the given options:
  • Option 1: θ increases and h also increases
    • This option is incorrect because if the contact angle θ increases (due to wax coating), the height h up to which water rises decreases.
  • Option 2: θ decreases and h also decreases
    • This option is incorrect because if the contact angle θ decreases, the height h up to which water rises increases.
  • Option 3: θ increases and h decreases
    • This option is correct because if the contact angle θ increases (due to wax coating), the height h up to which water rises decreases.
  • Option 4: θ decreases and h increases
    • This option is incorrect because if the contact angle θ decreases, the height h up to which water rises increases.

Therefore, the correct answer is option 3: θ increases and h decreases.

The forces at the interfaces of liquids, solids, and air are related to the surface tensions acting at those interfaces. The relation involving surface tensions can be derived from the Young-Laplace equation or using the force balance at the contact points.

At the solid-liquid interface, the tension S₃ and the angle of contact θ (also called the contact angle) are important in determining the net force. The force balance at the contact line gives the relationship between the surface tensions at the liquid-air, solid-air, and solid-liquid interfaces.

S₁cosθ + S₃ = S₂, where:

• S₁ is the surface tension at the liquid-air interface.
• S₂ is the surface tension at the solid-air interface.
• S₃ is the surface tension at the solid-liquid interface.
• θ is the contact angle at the solid-liquid interface.

∴ The relationship between the tensions at the liquid-air, solid-air, and solid-liquid interfaces is S₁cosθ + S₃ = S₂. Option 2) is correct.

Calculation:

Mass of water in capillary rise \(= Ah\rho\)

\(A=\) area of cross-section, \(h=\) height, \(\rho = \) density

\(\Rightarrow m = (\pi r^2)h\rho = \pi r^2 \times \dfrac{2\sigma \cos\theta}{r\rho g} \)

\(\Rightarrow m \propto r\)

\(\therefore\) Doubling radius \(\Rightarrow\)mass will also get doubled

\(m'=2 M\)

Calculation:

As the both points are at the surface of liquid and these points are in the open atmosphere.

So both point possess similar pressure and equal to 1 atm.

Hence the pressure difference will be zero

Concept:

Capillary Action

• When one end of a tube of small radius (known as a capillary tube) is dipped into a liquid, the liquid rises or is depressed in the tube. 
• If the contact angle is less than 90°, the liquid rises. 
• If it is more than 90°, it is depressed. 
•  Adhesive and cohesive forces are the main causes of this.
• Capillary rise or fall is given by,
• \(h = \frac{4σ cos θ }{\rho g d}\) --- (1)

• Where, h = Height of liquid column, σ = Surface Tension, d = diameter of capillary tube, θ = Angle of contact of the liquid, ρ = Density of liquid, g = Acceleration due to gravity = 9.81 m\s²

Calculation:

Given, diameter of capillary tube, d = 2 mm = 0.002 m, liquid rises in tube, h = 15 mm = 0.015 m, angle of contact, θ = 0

Specific gravity of the liquid = 0.8

Then the density of the liquid = 0.8 × 1000 = 800 kg/m³ 

From equation 1,

\(⇒ 0.015 = \frac{4σ cos ~0 }{800 \times 9.81\times 0.002}\)

⇒ σ = 0.05886 ≈ 0.06 N/m

CONCEPT:

Capillarity

• Capillary action is the ability of a fluid to flow through a narrow space without the application of an external force.
  • When a tube of very small diameter is dipped inside a fluid, we can see either a rise or a fall of fluid inside a tube.
  • If the fluid level increases in the tube it is called capillary rise and if the fluid level decreases it is called capillary fall.
  • Adhesive forces: Attractive forces between molecules of different types are called adhesive forces.
  • Cohesive forces: Attractive forces between molecules of the same types are called cohesive forces.

Surface tension: 

• Surface tension is the tension of the surface film of a liquid caused due to the attraction of the particles in the surface layer by the bulk of the liquid, which tends to minimize surface area.
• It is defined as the ratio of the surface force F to the length L along which the force acts.

​\(\Rightarrow T=\frac{F}{l}\)

Where T = surface tension

EXPLANATION:

• The shape of the liquid is actually controlled by two forces viz. surface tension and gravitational force.
  • When the size of the drop is small, surface tension dominates the gravitational force, which means the net force is due to surface tension.
  • The surface tension tries to minimize the surface area of the droplet and makes the droplet spherical.
• The cohesive force between the oil and the wick is more compared to the adhesive force of oil, so the oil rises through the wick due to capillarity.

• For capillary action, the diameter of the tube should be very small.

• The liquid rises in the capillary tube due to surface tension.

• But while drinking cold drinks, we need to create low pressure closer to the mouth and due to the pressure difference between the top and the bottom of the straw, cold drink rises. So the rise of cold drink in straw is not due to capillary action.

• Hence, option 3 is correct.

The correct answer is option 1) i.e. Adhesive forces must be greater than the cohesive forces

CONCEPT:

• Capillary action: Capillary action is the movement of a liquid along the surface of a solid due to the attraction of molecules of the liquid to the molecules of the solid.
  • For capillary action to take place, the force between the liquid and solid must be greater than the intermolecular forces of the liquid.
  • The force between two different types of molecules are called adhesive forces and the forces within the same type of molecules are called cohesive forces.

EXPLANATION:

• Capillary action occurs only when the liquid can move along the surface of another solid. This requires adhesive forces between the liquid and solid.
• If the cohesive forces within the liquid were greater, the surface tension of the liquid increases and it will try to occupy a lesser surface area possible.
• Hence, adhesive forces must be greater than the cohesive forces for capillary action to take place.

Concept:

The capillary tension causes the fluid to rise against the gravitational force, thus creating a capillary zone.

Capillarity or capillary action is the ability of a narrow tube to draw a liquid upwards against the force of gravity. The height of the liquid in a tube due to capillarity is expressed in m.

By knowing the surface tension σ, angle of contact ϴ, tube diameter d, and specific weight w the rise/depression of the liquid in the capillary tube can be analyzed.

\(h = \frac{{4\sigma cos\theta }}{{\rho gd}}\)

\(h=\frac{{4\sigma \cos \theta }}{{\rho gd}} \Rightarrow h\propto \frac{1}{d}\)

Important Points
For the plate,

\(\mathrm{h}=\frac{2\sigma \cos \theta}{\rho g \mathrm{~t}}\)

where, t = distance between the two plates

The correct answer is option 4) i.e. Capillarity.

CONCEPT:

• Capillary action: Capillary action is the movement of a liquid along the surface of a solid due to the attraction of molecules of the liquid to the molecules of the solid (surface tension).
  • For capillary action to take place, the adhesive force between the liquid and solid must be greater than the cohesive force of the liquid.

EXPLANATION:

• Plants have roots that run deep into the soil where water molecules are attracted to the root of the plants.
• When the attraction between the water molecule and roots (adhesion) exceeds the attraction between water molecules (cohesion), capillary action takes place.
•  This causes the water to move up from the ground through the narrow tube-like structure of roots.
• Therefore, the water rises in plant fibers due to capillarity.

​Additional Information

CONCEPT: 

• Capillarity is the process in which the liquid either ascend or descend  while placed in contact with any solid surfaces like tubes 
• Capillarity occurs due to adhesive and cohesive forces.
• Surface tension is the tendency of liquid to shrink the surface area to a minimum

EXPLANATION:

• From the given options except for the third option, all the other options can be explained using capillarity 
• Hence, option 3  is the answer

Concept:

• Capillary action: If one end of a capillary tube is put into a liquid that wets glass, it is found that the liquid rises into the capillary tube to a certain height.
• This rise is due to inward pull of surface tension acting on the surface which pushes the liquid into the capillary tube.
  • When the intermolecular interaction of the solvent itself is significantly inferior to the surface of the material it interacts with, capillary action occurs.
  • It happens only when the binding forces in the liquid are greater than the cohesive forces, which inevitably develop into surface tension.

The height of the liquid rises or fall (h) is given by

\({\rm{h}} = \frac{{2{\rm{\;T}}\cos {\rm{\theta }}}}{{{\rm{d\;\rho \;g}}}}\)

Where T = surface tension, θ = angle of contact, d = diameter of capillary tube, ρ = density of liquid, g = acceleration due gravity.

CONCEPT:

Capillary action:

• It is the ability of a fluid to flow through a narrow space without the application of an external force.
  • When a tube of very small diameter is dipped inside a fluid, we can see either a rise or a fall of fluid inside a tube.
  • If the fluid level increases in the tube it is called capillary rise and if the fluid level decreases it is called capillary fall.
• The reason for the capillary action is adhesive and cohesive forces.
   

• If the adhesive force is more compared to cohesive force, then there will be the capillary rise and the meniscus will be of concave shape.
• If the cohesive force is more compared to adhesive force, then there will be capillary fall and the meniscus will be of convex shape.
• For capillary rise the angle of contact is less than 90° and for capillary fall the angle of contact is greater than 90°.

EXPLANATION:

• As we know that if the adhesive force is more compared to cohesive force, then there will be the capillary rise and the meniscus will be of concave shape.
• So the angle of contact is less than 90° for the capillary rise.
• If the cohesive force is more compared to adhesive force, then there will be capillary fall and the meniscus will be of convex shape.
• So the angle of contact is greater than 90° for capillary fall. Hence, option 1 is correct.

The correct answer is option 1) i.e. acute.

CONCEPT:

• Capillary action: The rise of a column of liquid within a fine capillary tube due to the surface tension of the liquid is called capillary action.
  • Consider a capillary tube of radius r dipped in a liquid of density ρ. Let us assume that the liquid rises to a height of h in the tube due to the surface tension σ.

 
θ" tabindex="0">θθ is the contact angle made by the liquid meniscus with the capillary tube's surface.

On balancing the forces in the liquid column of height h,

⇒ Weight of the water in column = Upwards force due to surface tension

Mass of water × g = σ cos θ × perimeter

Density × volume × g = σ cos θ × 2πr

ρ × πr²h × g = σ cos θ × 2πr

Capillary rise, h = \(\frac{2σ \cosθ}{ρ g r}\)

EXPLANATION:

• Capillary rise is dependent on θ. Therefore capillary rise depends on the values of cos θ.
• For a rise in the liquid column, the value of capillary rise must be positive. This is possible only when 0° < θ < 90° i.e. when θ is an acute angle.
• Hence, the liquid rises in a capillary tube if the angle of contact is acute.

Given:

The diameter of the capillary (d) = 4 mm or (0.004 m)

Reynolds's number of the tube (R) = 1000

Co-efficient of viscosity for the water (η) = 0.02 poise

Concept:

We get to know about the laminar and turbulent nature of flow through the Reynolds number.

Critical velocity is the maximum velocity above which the nature of flow no longer remains Laminar.

Formula:

The Reynolds number is given by : \(R = \frac{ρ v d}{η}\)

Where v is the average velocity of the flow.

1 Poise = 0.1 Pa-s

Density of water (ρ) = 1000 kg/m³

Calculation:

• 0.02 poise =  0.02 × 0.1 Pa-s

= 0.002 Pa-s

∵ R = ρvd/η 

⇒ v = Rη/ρd

⇒ v = (1000 × 0.002)/(1000 × 0.004)

= 0.5 m/s or 50 cm/s

• Now the maximum velocity will be double the average velocity of the flow.

So, v_max = 2v =  2 × 50

⇒ vmax = 100 cm/s