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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Some Mechanical Properties of Matter

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Some Mechanical Properties of Matter

As water droplets combine to form a larger drop,

As water droplets combine to form a larger drop,

Options

  1. Aenergy may be either liberated or absorbed depending on the nature of the liquid
  2. Benergy is neither liberated nor absorbed
  3. Cenergy is liberated
  4. Denergy is absorbed

Correct answer

C. energy is liberated

Step-by-step solution

When nn small droplets of radius rr combine to form a single large drop of radius RR, the total volume remains constant.

43πR3=n×43πr3⇒R=n1/3r\dfrac{4}{3}\pi R^3 = n \times \dfrac{4}{3}\pi r^3 \Rightarrow R = n^{1/3}r

The initial total surface area is Ai=n×4πr2A_i = n \times 4\pi r^2.

The final surface area is Af=4πR2=4πn2/3r2A_f = 4\pi R^2 = 4\pi n^{2/3}r^2.

Since n>n2/3n > n^{2/3} for n>1n > 1, the total surface area decreases (Af<AiA_f < A_i).

Surface energy is directly proportional to the surface area (U=T×AU = T \times A, where TT is surface tension). As the surface area decreases, the total surface energy of the system decreases.

This loss in surface energy is liberated to the surroundings.
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