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]

0%

(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]

0%

(8)

$△ P = \frac{4 T}{R}$

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

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

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]

0%

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]

0%

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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]

0%

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]

0%

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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]