Fluid Mechanics | Surface Tension And Viscosity | JEE Main previous year questions with Solutions

Q 1 :

Given below are two statements:

Statement I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be 0°.

Statement II: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.

In the light of the above statement, choose the correct answer from the options given below. [2024]

Both Statement I and Statement II are true
Statement I is true and Statement II is false
Statement I is false but Statement II is true
Both Statement I and Statement II are false

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(3)

Statement I is false because capillary rise is zero for angle of contact 90°

Capillary rise, $h = \frac{2 T \cos θ}{ρ g r},$ If $θ = 0^{o}$ then rise is non-zero

Statement II is true because angle of contact depends on both liquid and solid.

Q 2 :

Pressure inside a soap bubble is greater than the pressure outside by an amount

(Given: R = Radius of bubble, S = Surface tension of bubble) [2024]

$\frac{4 R}{S}$
$\frac{4 S}{R}$
$\frac{2 S}{R}$
$\frac{S}{R}$

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(2)

$P_{e x} = P_{i n} - P_{o u t}$

$P_{i n} = P_{o u t} + P_{e x}$

$P_{i n} = P_{o u t} + \frac{4 S}{R}$

Q 3 :

Given below are two statements:

Statement I: If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.

Statement II: If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.

In the light of the above statements, choose the most appropriate from the options given below [2024]

Both Statement I and Statement II are true
Both Statement I and Statement II are false
Statement I is true but Statement II is false
Statement I is false but Statement II is true

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(3)

Surface tension decreases with increase in temperature

The height of capillary rise is $h = 2 T$ $\cos$ $θ / ρ g r$

The height of capillary rise will be smaller in hot water and larger in cold water.

Q 4 :

A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is $8 \times 10^{3}$ $k g$ $m^{- 3}$ and surface tension of soap solution is 0.28 $N m^{- 1}$ , then diameter of the soap bubble is ______ cm. (if $g = 10$ $m s^{- 2}$ ) [2024]

(7) $ρ g h = \frac{4 S}{R} \Rightarrow R = \frac{4 \times 0.28}{8 \times 10^{3} \times 10 \times 4 \times 10^{- 4}}$

$\Rightarrow \frac{0.28}{8} m = \frac{28}{8} c m$

$\Rightarrow R = 3.5 cm$

$Diameter = 7 cm$

Q 5 :

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is [2024]

1 : 9
1 : 3
1 : 81
1 : 27

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(4)

Excess pressure in soap bubble $= \frac{4 S}{R}$

Given $P_{1} = 3 P_{2}$ $∴$ $P_{1} = \frac{4 S}{R_{1}} and P_{2} = \frac{4 S}{R_{2}}$

$3 P_{2} = \frac{4 S}{R_{1}}; R_{1} = \frac{4 S}{3 P_{2}}; R_{2} = \frac{4 S}{P_{2}}$

$\Rightarrow \frac{R_{1}}{R_{2}} = \frac{4 S}{3 P_{2}} \times \frac{P_{2}}{4 S} = \frac{1}{3}$

Ratio between the volumes $\frac{V_{1}}{V_{2}} = \frac{\frac{4}{3} π R_{1}^{3}}{\frac{4}{3} π R_{2}^{3}} = \frac{1}{27}$

Q 6 :

Two liquids A and B have $θ_{A}$ and $θ_{B}$ as contact angles in a capillary tube. If $K = \cos θ_{A} / \cos θ_{B}$ , then identify the correct statement: [2025]

K is negative, then liquid A and liquid B have convex meniscus.
K is negative, then liquid A and liquid B have concave meniscus.
K is negative, then liquid A has concave meniscus and liquid B has convex meniscus.
K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.

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(3)

For concave meniscus $θ_{A}$ < 90°

For convex meniscus $θ_{B}$ > 90°

$K = \frac{\cos θ_{A}}{\cos θ_{B}} < 0$

K is negative when cos $θ_{A}$ and cos $θ_{B}$ are of opposite signs.

Q 7 :

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle 0°) with 30° inclined with vertical. The length of water risen in the capillary is _____ cm. (Take g = 9.8 $m / s^{2}$ ) [2025]

$\frac{82}{5}$
$\frac{57}{2}$
$\frac{71}{5}$
$\frac{68}{5}$

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(1)

$h = \frac{2 T \cos θ}{ρ g r} = \frac{2 \times 70 \times 1}{1 \times 980 \times 10^{- 2}} = \frac{100}{7} cm$

$\sin 60 ° = \frac{h}{l} \Rightarrow l = \frac{h \times 2}{\sqrt{3}}$

$l = \frac{100}{7} \times \frac{2}{\sqrt{3}} = \frac{200}{7 \times \sqrt{3}} = 16.49 cm$

Q 8 :

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is n times the volume of the bubble B, then, the value of n is ________. [2025]

(8)

$△ P = \frac{4 T}{R}$

$\frac{R_{A}}{R_{B}} = \frac{△ P_{B}}{△ P_{A}} = 2$

$\frac{V_{A}}{V_{B}} = {(\frac{R_{A}}{R_{B}})}^{3} = 8$

Q 9 :

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is 5 cm. If the tube is dipped in a similar manner in another liquid B of surface tension and density double the values of liquid A, the height of liquid column raised in liquid B would be ___ m. [2023]

0.20
0.5
0.05
0.10

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(3)

$h = \frac{2 S \cos θ}{r ρ g}$

$∴$ $\frac{h_{1}}{h_{2}} = \frac{S_{1}}{S_{2}} \frac{ρ_{2}}{ρ_{1}}$

$\frac{5}{h_{2}} = [\frac{1}{2}] [\frac{2}{1}]$ $\Rightarrow h_{2} = 5 cm = 0.05 m$

Q 10 :

Given below are two statements:

Statement I: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.

Statement II: The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.

In the light of the above statements, choose the correct answer from the options given below: [2023]

Statement I is false but Statement II is true.
Both Statement I and Statement II are false.
Both Statement I and Statement II are true.
Statement I is true but Statement II is false.

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(4)

Statement I is correct as we know contact angle depends on cohesive and adhesive forces.

Statement II is incorrect because height of liquid is given by $h = \frac{2 T \cos θ}{ρ g r}$ where $r$ is the radius of the tube (assuming the length of the capillary is sufficient).

Q 11 :

Surface tension of two liquids (having same densities), $T_{1} and T_{2}$ , are measured using capillary rise method utilizing two tubes with inner radii of $r_{1} and r_{2}$ where $r_{1} > r_{2}$ . The measured liquid heights in these tubes are $h_{1} and h_{2}$ respectively. [Ignore the weight of the liquid about the lowest point of meniscus.]

The heights $h_{1} and h_{2}$ and surface tensions $T_{1} and T_{2}$ satisfy the relation: [2026]

$h_{1} > h_{2} and T_{1} < T_{2}$
$h_{1} < h_{2} and T_{1} = T_{2}$
$h_{1} > h_{2} and T_{1} = T_{2}$
$h_{1} = h_{2} and T_{1} = T_{2}$

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(2)

$h = \frac{2 T}{ρ g r}$

$h \propto \frac{1}{r}$

$If r_{1} > r_{2} \Rightarrow h_{2} > h_{1}$

Q 12 :

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.

Statement-1: A capillary is dipped in a liquid and liquid rises to a height h in it. As the temperature of the liquid is raised, the height h increases (if the density of the liquid and the angle of contact remain the same).

Statement-2: Surface tension of a liquid decreases with the rise in its temperature.

Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1.
Statement-1 is false, Statement-2 is true.
Statement-1 is true, Statement-2 is false.
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1.

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(2)

Surface tension of a liquid decreases with the rise in temperature. At the boiling point of liquid, surface tension is zero. Capillary rise $h = \frac{2 T \cos θ}{r d g}$

As surface tension T decreases with rise in temperature

hence capillary rise also decreases

Q 13 :

A container is partially filled with a liquid of density $ρ_{2}$ . A capillary tube of radius $r$ is vertically inserted in this liquid. Now another liquid of density $ρ_{1} (ρ_{1} < ρ_{2})$ is slowly poured in the container to a height $h$ as shown. There is only denser liquid in the capillary tube. The rise of denser liquid in the capillary tube is also $h$ . Assuming zero contact angle, the surface tension of heavier liquid is

$r ρ_{2} g h$
$2 π r ρ_{2} g h$
$\frac{r}{2} (ρ_{2} - ρ_{1}) g h$
$2 π r (ρ_{2} - ρ_{1}) g h$

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(3)

$P_{0} + ρ_{1} g h - ρ_{2} g h + \frac{2 T}{r} = P_{0} \Rightarrow T = \frac{r}{2} (ρ_{2} - ρ_{1}) g h$

Q 14 :

Pressure inside a soap bubble is greater than the pressure outside by an amount:

(given : R = Radius of bubble, S = Surface tension of bubble)

$\frac{S}{R}$
$\frac{4 S}{R}$
$\frac{3 R}{S}$
$\frac{6 R}{S}$

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(2)

$EXCESS PRESSURE = \frac{4 S}{R}$

Topic Question Set

Q 2 :

Pressure inside a soap bubble is greater than the pressure outside by an amount

(Given: R = Radius of bubble, S = Surface tension of bubble) [2024]

Q 4 :

A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is $8 \times 10^{3}$ $k g$ $m^{- 3}$ and surface tension of soap solution is 0.28 $N m^{- 1}$ , then diameter of the soap bubble is ______ cm. (if $g = 10$ $m s^{- 2}$ ) [2024]

Q 5 :

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is [2024]

Q 6 :

Two liquids A and B have $θ_{A}$ and $θ_{B}$ as contact angles in a capillary tube. If $K = \cos θ_{A} / \cos θ_{B}$ , then identify the correct statement: [2025]

Q 7 :

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle 0°) with 30° inclined with vertical. The length of water risen in the capillary is _____ cm. (Take g = 9.8 $m / s^{2}$ ) [2025]

Q 8 :

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is n times the volume of the bubble B, then, the value of n is ________. [2025]

Q 14 :

Pressure inside a soap bubble is greater than the pressure outside by an amount:

(given : R = Radius of bubble, S = Surface tension of bubble)

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Topic Question Set

Q 2 : Pressure inside a soap bubble is greater than the pressure outside by an amount (Given: R = Radius of bubble, S = Surface tension of bubble) [2024]

Q 4 : A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is 8×103 kg m-3 and surface tension of soap solution is 0.28 Nm-1, then diameter of the soap bubble is ______ cm. (if g=10 ms-2) [2024]

Q 5 : The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is [2024]

Q 6 : Two liquids A and B have θA and θB as contact angles in a capillary tube. If K=cos θA/cos θB, then identify the correct statement: [2025]

Q 7 : A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle 0°) with 30° inclined with vertical. The length of water risen in the capillary is _____ cm. (Take g = 9.8 m/s2) [2025]

Q 8 : The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is n times the volume of the bubble B, then, the value of n is ________. [2025]

Q 14 : Pressure inside a soap bubble is greater than the pressure outside by an amount: (given : R = Radius of bubble, S = Surface tension of bubble)

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Q 2 :

Pressure inside a soap bubble is greater than the pressure outside by an amount

(Given: R = Radius of bubble, S = Surface tension of bubble) [2024]

Q 4 :

A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is $8 \times 10^{3}$ $k g$ $m^{- 3}$ and surface tension of soap solution is 0.28 $N m^{- 1}$ , then diameter of the soap bubble is ______ cm. (if $g = 10$ $m s^{- 2}$ ) [2024]

Q 5 :

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is [2024]

Q 6 :

Two liquids A and B have $θ_{A}$ and $θ_{B}$ as contact angles in a capillary tube. If $K = \cos θ_{A} / \cos θ_{B}$ , then identify the correct statement: [2025]

Q 7 :

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle 0°) with 30° inclined with vertical. The length of water risen in the capillary is _____ cm. (Take g = 9.8 $m / s^{2}$ ) [2025]

Q 8 :

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is n times the volume of the bubble B, then, the value of n is ________. [2025]

Q 14 :

Pressure inside a soap bubble is greater than the pressure outside by an amount:

(given : R = Radius of bubble, S = Surface tension of bubble)