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Mechanical Properties of Fluids

Surface tension

Several spherical drops of a liquid each of radius r coalesce

Question

Hard

Solving time: 4 mins

Several spherical drops of a liquid each of radius $r$ coalesce to form a single drop of radius $R$ . If $T$ is the surface tension, then the energy liberated will be :

4 π R^{3} T (\frac{1}{r} - \frac{1}{R})

2 π R^{3} T (\frac{1}{r} - \frac{1}{R})

\frac{4}{3} π r^{3} T (\frac{1}{r} - \frac{1}{R})

2 π R^{3} T (\frac{1}{R} - \frac{1}{r})

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Oliver Discussed

Several spherical drops of a liquid each of radius

r

coalesce to form a single drop of radius

R

. If

T

is the surface tension, then the energy liberated will be :

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

Volume of spherical drops

\Rightarrow n (\frac{4}{3} π r^{3}) = \frac{4}{3} π R^{3}

So,

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

Energy Liberated,

u = T Δ A

= T [4 π R^{2} - n 4 π r^{2}] = 4 π T [R^{2} - nr^{2}] = 4 π T [R^{2} - \frac{R ^{3}}{r ^{3}} r^{2}] = 4 π R^{3} T [\frac{1}{R} - \frac{1}{r}] = 3 (\frac{4}{3} π R^{3}) T (\frac{1}{R} - \frac{1}{r}) u = 4 π TR 3 (\frac{1}{R} - \frac{1}{r}) (R > r) u = 4 π TR R^{3} (\frac{1}{r} - \frac{1}{R}) (r > R)

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Question Text	Several spherical drops of a liquid each of radius $r$ coalesce to form a single drop of radius $R$ . If $T$ is the surface tension, then the energy liberated will be :
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	115

Several spherical drops of a liquid each of radius $r$ coalesce to form a single drop of radius $R$ . If $T$ is the surface tension, then the energy liberated will be :

Text solutionVerified

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