SATHEE: Mechanical Properties of Fluids

Mechanical Properties of Fluids - Result Question 17

17. A certain number of spherical drops of a liquid of radius ’ $r$ ’ coalesce to form a single drop of radius ’ $R$ ’ and volume ’ $V$ ‘. If ’ $T$ ’ is the surface tension of the liquid, then :

[2014]

(a) energy $= 4 V T (\frac{1}{r} - \frac{1}{R})$ is released

(b) energy $= 3 V T (\frac{1}{r} + \frac{1}{R})$ is absorbed

(d) energy is neither released nor absorbed

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Answer:

Correct Answer: 17. (c)

Solution:

$\Rightarrow n = \frac{R^{3}}{r^{3}}$

Change in energy $= T Δ A = T [4 π R^{2} - n 4 π r^{2}]$

$= 4 π T [R^{2} - \frac{R^{3}}{r^{3}} r^{2}]$

$= 3 (\frac{4}{3} π R^{3}) T [\frac{1}{R} - \frac{1}{r}]$

$=3 VT\frac{1}{R}-\frac{1}{r}$

$= 3 V T [\frac{1}{r} - \frac{1}{R}]$ is released

Energy released when $n$ drops of radius $r$ coalesec to form a body drop of radius $R$ ,

Energy released $= 4 π R^{3} T [\frac{1}{r} \frac{- 1}{R}]$

If this energy get converted into kinetic energy of big drop, then

$\begin{aligned} \frac{1}{2} m v^{2} = 4 π R^{3} T [\frac{1}{r} \frac{- 1}{R}] \\ \Rightarrow \frac{1}{2} [\frac{4}{3} π R^{3} d] V^{2} = 4 π R^{3} T [\frac{1}{r} \frac{- 1}{R}] \\ \Rightarrow v 2 = \frac{6 T}{d} [\frac{1}{r} \frac{- 1}{R}] \end{aligned}$

$\Rightarrow$ Velocity of big drop $V = \sqrt{\frac{6 T}{d} (\frac{1}{r} \frac{- 1}{R})}$

(Where, $d =$ density of big liquid drop)

Mechanical Properties of Fluids - Result Question 17

17. A certain number of spherical drops of a liquid of radius ’ $r$ ’ coalesce to form a single drop of radius ’ $R$ ’ and volume ’ $V$ ‘. If ’ $T$ ’ is the surface tension of the liquid, then :

Answer:

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Mechanical Properties of Fluids - Result Question 17

17. A certain number of spherical drops of a liquid of radius ’ r ’ coalesce to form a single drop of radius ’ R ’ and volume ’ V ‘. If ’ T ’ is the surface tension of the liquid, then :

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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17. A certain number of spherical drops of a liquid of radius ’ $r$ ’ coalesce to form a single drop of radius ’ $R$ ’ and volume ’ $V$ ‘. If ’ $T$ ’ is the surface tension of the liquid, then :