Surface tension MCQ Quiz - Objective Question with Answer for Surface tension - Download Free PDF

Correct option is: (2) d²y/dx² = (ρg / S) y

Explanation:

Curvature = 1 / ROC = |d²y/dx²| / (1 + (dy/dx)²)^3/2 ≈ |d²y/dx²| / (1 + 0)^3/2 = d²y/dx²

(dy/dx) ≈ tan θ ≈ 0 (small angle approximation)

Change in pressure, ΔP = S × curvature

ΔP = S × d²y/dx²

Also, ΔP = ρgy

⇒ ρgy = S × d²y/dx²

⇒ d²y/dx² = (ρg / S) y

Concept:

Surface tension: 

• Surface tension is the property by virtue of which liquid tires to minimize its free surface area.
• In spherical shape the surface area is minimum and for this reason, the raindrops are spherical.
• Surface tension is measured as the force acting per unit length of an imaginary line drawn on the liquid surface.
  \(Surface\;tension = \frac{{Force}}{{length}}\)

• Temperature: If temperature increases then the surface tension of a liquid decreases.
• Soluble Impurities: In the case of less soluble impurities, the surface tension decreases. But, for highly soluble impurities in the liquid the surface tension increases.

Explanation:

Hot water is less viscous then cold water.

Surfactant reduces surface tension. 

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).

Calculation:

Given,

R₁ = 3 cm = 3 × 10⁻² m

R₂ = 5 cm = 5 × 10⁻² m

T = 0.03 N/m (Surface tension)

Original surface area = 2 × 4πR₁

For second bubble = 2 × 4πR₂

Work done = Surface tension × extension in area

Work done = T × ΔA

Substitute the values:

Work done = 0.03 × 2[4πR₂² - 4πR₁²]

Work done = 0.03 × 8π[(5)² - (3)²] × 10⁻⁴

Work done = 0.03 × 8π × 16 × 10⁻⁴

Work done = 0.384π × 10⁻³ J

Hence, the work done is approximately 0.4π mJ.

CONCEPT:

Surface Tension

Surface tension is a property of liquids that makes them acquire the least surface area possible. It is the force per unit length acting along the surface of a liquid.

The work done in increasing the surface area of a liquid film is given by the product of the surface tension and the change in surface area.

EXPLANATION:

Let's calculate the surface tension of the soap film:

The initial dimensions of the soap film are 10 cm × 6 cm. Hence, the initial area (A₁) is:

A₁ = 10 cm × 6 cm = 60 cm²

The final dimensions of the soap film are 10 cm × 11 cm. Hence, the final area (A₂) is:

A₂ = 10 cm × 11 cm = 110 cm²

The change in area (ΔA) is:

ΔA = A₂ - A₁ = 110 cm² - 60 cm² = 50 cm²

The work done (W) in increasing the size of the soap film is given as 3 × 10^-4 joule.

The surface tension (γ) is calculated using the formula:

W = γ × ΔA

Rearranging the formula for γ gives:

γ = W / ΔA

Substitute the values:

γ = (3 × 10^-4 joule) / (50 cm²)

Note: 1 cm² = 10^-4 m², so 50 cm² = 50 × 10^-4 m²

γ = (3 × 10^-4 joule) / (50 × 10^-4 m²)

γ = (3 / 50) N/m

γ = 0.06 N/m

Therefore, the correct answer is option 2: 3.0 × 10^-2 N/m.

CONCEPT:

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.
• When impurities are added to the water the intermolecular distance increases due to which Van der Wall forces decrease, so the surface tension decreases on adding impurities to the water.

EXPLANATION:

• When impurities are dissolved in water, the surface tension of water decreases.
• Hence, when camphor is dissolved in water, surface tension will decrease. 
• As different amounts of camphor are dissolved from different sides so Camphor becomes non-symmetrical.
• Therefore surface tension will be different on different sides of the camphor which sets up an unbalanced force on the camphor due to which it dances on the surface of the water. Hence, option 2 is correct.

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.

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

\({\rm{h}} = \frac{{4{\rm{\;T}}\cos {\rm{\theta }}}}{{{\rm{d\;\rho \;g}}}}\)

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

Explanation:

Hence the rise in capillary action is due to surface tension.

CONCEPT:

• Surface tension: The property by virtue of which liquid tries to minimize its free surface area is called surface tension.
• In spherical shape the surface area is minimum and for this reason, the raindrops are spherical.
• Two factors can affect the surface tension of a liquid. The factors are;
  • Temperature: If temperature increases then the surface tension of a liquid decreases.
  • Soluble Impurities: In the case of less soluble impurities, the surface tension decreases. But, for highly soluble impurities in the liquid, the surface tension increases.
• Examples:
  • When kerosene oil is sprinkled on the water the surface decreases and for this reason, the mosquito larvas die due to sinking in the water.
  • Warm soup is tasty because for high temperatures the surface tension becomes low and spread equally over the tongue.

EXPLANATION:

• Intermolecular force: The force between the molecules of the fluid is called intermolecular force
• The intermolecular force is responsible for the viscosity of the fluid. 
• If the intermolecular force is more then the viscosity will be more and if it is less then the viscosity will be less.
• Real fluids possess some finite value of surface tension because the real fluids have a significant value of the intermolecular forces between the molecules.
• Whereas in the case of an ideal fluid, the intermolecular forces are assumed to be very less that's why the ideal fluids have zero value surface tension. So option 2 is correct.
• Separation of oil and water takes place due to surface tension. 

CONCEPT:

• The property of a liquid due to which its free surface tries to have the minimum surface area and behaves as if it were under tension somewhat like a stretched elastic membrane is called surface tension.
• The surface tension of a liquid is measured by the force acting per unit length on either side of an imaginary line drawn on the free surface of the liquid.

\(Surface\;tension = \frac{{Force}}{{length}}\)

EXPLANATION:

• Hair of shaving brush/painting brush when dipped in water spread out, but as soon as it is taken out, its hair sticks together it is due to surface tension. Hence, option 2 is correct.

CONCEPT:

Surface tension (S):

• It is the property by virtue of which the free surface of a liquid at rest behaves like an elastic stretched membrane tending to contract so as to occupy the minimum surface area.
• Surface tension is measured as the force acting per unit length of an imaginary line drawn on the liquid surface.
  \(Surface\;tension (S) = \frac{{Force (F)}}{{length(l)}}\)

• A small liquid drop has a spherical shape, as due to surface tension the liquid surface tries to have the minimum surface area and for a given volume, the sphere has a minimum surface area. Therefore option 3 is correct.

Applications of Surface Tension

• The warm soup tastes tasty because its surface tension is low at high temperatures and the soup spreads on all parts of the tongue.
• The phenomenon of the rising or fall of liquid level inside a capillary tube, when it is dipped in the liquid, is called capillary action.
• The capillary actions are due to surface tension.
• Capillary action draws the ink to the tips of fountain pen nibs from a reservoir or cartridge within the pen.

The correct answer is option 4) i.e. surface tension.

CONCEPT:

• Surface tension is the tendency of water molecules to adhere to each other so as to form the minimum surface area possible.
  • This is a result of cohesion between water molecules.
  • Towards the interface of water with air, there will be no cohesive forces. Hence the net force acts downwards.
  • The top surface of the water will now act like a stretched membrane.

EXPLANATION:

• When an iron needle is placed on water, the stretched membrane of water prevents the iron nail from sinking.
• The stretched membrane occurs due to the surface tension of water.

Hence, an iron needle floats on the surface of the water because of surface tension.

Confusion Points

• Not all substances can float on water due to surface tension. Only objects whose weight is lesser than the force due to surface tension will float.
• The density of the iron needle is greater than that of water, but it does not sink because the weight is comparatively small to break the surface tension of the water surface.

CONCEPT:​

• Surface tension: The property of liquid surfaces to shrink into the minimum surface area possible is known as surface tension.
• Work done to blow a bubble, make a drop is calculated by

W = surface tension × surface area of bubble or drop

CALCULATION:

Work done to blow a bubble = Surface tension × surface area 

Since the soap bubble is in the air so there will be two surfaces in contact with the air (inside and outside)

Work done to blow a bubble = Surface tension × 2 × surface area of the bubble

Work done to blow a bubble of radius 2R

W = T × 2 × A

W = T × 2 × (4π(2R)²)

W = 32TπR2 .....................(i)

Work done to blow a bubble of radius R

W' = T × 2 × A = T × 2 × (4πR2)

W' = 8TπR2 ........................(ii)

Eq (ii) / eq (i)

\( {W'\over W}= {8T \pi R^2 \over 32T \pi R^2 }\)

\( {W'\over W}= {1\over 4 }\)

\( {W'}= {W\over 4 }\)

So the correct answer is option 4.

CONCEPT:

• Surface tension: The property by virtue of which liquid tries to minimize its free surface area is called surface tension.
  • In spherical shape the surface area is minimum and for this reason, the raindrops are spherical.

• 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.

EXPLANATION:

• There is an attractive force between molecules of the same type and due to this force, it tries to minimize the area.
• This force is a cohesive force and this property is called surface tension. 
• Thus the surface tension is due to cohesive molecular forces. So option 1 is correct.
• The gravitational force is between two masses separated by a distance.
• The nuclear force is between two nuclides in the nucleus of an atom.
• The electrical force is between two charges separated by a distance.

CONCEPT:

• Surface tension: The property by virtue of which liquid tries to minimize its free surface area is called surface tension.
  • It is denoted by S or T.

Surface tension is given by:

S or T = F/L

where F is force and L is the length of contact.

EXPLANATION:

• The insect can move on the surface of water due to the surface tension of water. So option 3 is correct.
• The weight of the insect and structure of their feet in combination with the surface tension of water allows some insects to walk on water.
• Here the weight is balanced by the surface tension force.

CONCEPT:

• The property of a liquid due to which its free surface tries to have the minimum surface area and behaves as if it were under tension somewhat like a stretched elastic membrane is called surface tension.
• The surface tension of a liquid is measured by the force acting per unit length on either side of an imaginary line drawn on the free surface of the liquid.

\(Surface\;tension = \frac{{Force}}{{length}}\)

EXPLANATION:

• When hair is dipped in water it spread out, but as soon as it is taken out, its sticks together are due to surface tension.  
• This is caused because as we remove the hair from water, water molecules that are attached to hairs will try to reduce the surface area because of cohesive force between them and this creates tension along the surface and hence hairs cling together.