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

Q 1 :
Given below are two statements:

Statement (I):Viscosity of gases is greater than that of liquids.

Statement (II): Surface tension of a liquid decreases due to the presence of insoluble impurities.

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

Statement I is correct but statement II is incorrect
Statement I is incorrect but Statement II is correct
Both Statement I and Statement II are incorrect
Both Statement I and Statement II are correct

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2

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4

(B) Gases have less viscosity.

Due to insoluble impurities like detergent, surface tension decreases.

Q 2 :
A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be [2024]

$4 {πR}^{2} T$
$8 {πR}^{2} T$
$3 {πR}^{2} T$
$1 / 8 {πR}^{2} T$

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2

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4

(B) Volume of liquid of drops should be constant,

$\frac{4}{3} {πR}^{3} = 27 \times \frac{4}{3} \times {πr}^{3}$

$R^{3} = 27 r^{3} \Rightarrow R = 3 r$

$r = \frac{R}{3} \Rightarrow r^{2} = \frac{R^{2}}{9}$

Work done = $T \cdot ∆ A$

$= 27 T (4 {πr}^{2}) - T 4 {πR}^{2}$

$= 27 T 4 π \frac{R^{2}}{9} - 4 {πR}^{2} T = 8 {πR}^{2} T$

Q 3 :
A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become [2024]

100 times
10 times
$\frac{1}{100}$ th
$\frac{1}{10}$ th

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(D) Lets say radius of small droplets is $r$ and that of big drop is R,

By conservation of volume:

$\frac{4}{3} {πR}^{3} = 1000 \frac{4}{3} {πr}^{3} \Rightarrow R = 10 r$

$∴$ Surface energy of 1000 droplets

$U_{i} = 1000 (4 {πr}^{2} S)$

$U_{f} = 4 π R^{2} = 100 (4 {πr}^{2} S)$

$U_{f} = \frac{1}{10} U_{i}$

Q 4 :
A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is _______ cm. Take $(π = \frac{22}{7})$ [2024]

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(7) $Δ W = 2 T \cdot 4 π r_{2}^{2} - 2 T \cdot 4 π r_{1}^{2}$

$r_{2}^{2} - r_{1}^{2} = \frac{Δ W}{8 T π} = \frac{36960 \times 7}{8 \times 40 \times 22} = 36.75$

$r_{2}^{2} = 36.75 + \frac{49}{4} = 49 \Rightarrow r_{2} = 7 cm$

Q 5 :
A big drop is formed by coalescing 1000 small identical drops of water. If $E_{1}$ be the total surface energy of 1000 small drops of water and $E_{2}$ be the surface energy of single big drop of water, the $E_{1} : E_{0}$ is $x : 1$ where $x =$ __________ . [2024]

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(10) Let radius of small drops = r

Let radius of big drops = R

Here volume will remain conserve (volume conservation)

$∴ (1000) V_{s} = (1) V_{b} \to volume of big drop$

$Volume of small drop \Rightarrow 10^{3} (\frac{4}{3} π r^{3}) = \frac{4}{3} π R^{3}$

$R = 10 r$

$We know, surface tension = \frac{Surface energy}{Area}$

$∴ Surface energy = (Surface tension) (Area)$

$\Rightarrow ε_{1} = T \times 4 π r^{2} \times 10^{3}$

$ε_{2} = T \times 4 π R^{2}$

$∴ \frac{ε_{1}}{ε_{2}} = \frac{(10^{3}) (r^{2})}{R^{2}} = \frac{(10^{3}) r^{2}}{{(10 r)}^{2}} = \frac{10}{1}$

$\frac{ε_{1}}{ε_{2}} = \frac{10}{1} = \frac{X}{1},$

$∴ x = 10$

Topic Question Set

Q 2 :
A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be [2024]

Q 3 :
A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become [2024]

Q 4 :
A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is _______ cm. Take $(π = \frac{22}{7})$ [2024]

0%

Q 5 :
A big drop is formed by coalescing 1000 small identical drops of water. If $E_{1}$ be the total surface energy of 1000 small drops of water and $E_{2}$ be the surface energy of single big drop of water, the $E_{1} : E_{0}$ is $x : 1$ where $x =$ __________ . [2024]

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Topic Question Set

Q 2 : A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be [2024]

Q 3 : A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become [2024]

Q 4 : A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is _______ cm. Take (π=227) [2024]

0%

Q 5 : A big drop is formed by coalescing 1000 small identical drops of water. If E1 be the total surface energy of 1000 small drops of water and E2 be the surface energy of single big drop of water, the E1:E0 is x:1 where x= __________ . [2024]

0%

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Q 2 :
A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be [2024]

Q 3 :
A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become [2024]

Q 4 :
A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is _______ cm. Take $(π = \frac{22}{7})$ [2024]

Q 5 :
A big drop is formed by coalescing 1000 small identical drops of water. If $E_{1}$ be the total surface energy of 1000 small drops of water and $E_{2}$ be the surface energy of single big drop of water, the $E_{1} : E_{0}$ is $x : 1$ where $x =$ __________ . [2024]