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Change in surface energy when a drop splits into droplets or droplets coalesce

This type of question, asked 10 times: 2021 Paper 25, 28 Jun 2022, 26 Jul 2022, 31 Jan 2023, 1 Feb 2023, 29 Jan 2024, 24 Jan 2025, 2 Apr 2025, 2 Apr 2026 S1, 5 Apr 2026 S2. All 10 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 25

    15
    A large number of water drops, each of radius rr, combine to have a drop of radius RR. If the surface tension is TT and mechanical equivalent of heat is JJ, the rise in heat energy per unit volume will be:

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  2. Question 2

    28 Jun 2022

    6
    A water drop of diameter 2 cm2\text{ }cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m0.075\text{ }N/m. In this process the gain in surface energy will be:

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  3. Question 3

    26 Jul 2022

    15
    A water drop of radius 1 cm1\text{ }cm is broken into 729 equal droplets. If surface tension of water is 75dyne/cm75dyne/cm, then the gain in surface energy upto first decimal place will be: [Given π=3.14\pi = 3.14 ]

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  4. Question 4

    31 Jan 2023

    9
    If 1000 droplets of water of surface tension 0.07 N/m0.07\text{ }N/m, having same radius 1 mm1\text{ }mm each, combine to form a single drop. In the process the released surface energy is- (Take π=227\pi =\frac{22}{7} )

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  5. Question 5

    1 Feb 2023

    3
    A mercury drop of radius 10−3 m10^{- 3}\text{ }m is broken into 125 equal size droplets. Surface tension of mercury is 0.45Nm−10.45Nm^{- 1}. The gain in surface energy is:

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  6. Question 6

    29 Jan 2024

    101
    A small liquid drop of radius RR is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be :

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  7. Question 7

    24 Jan 2025

    7
    The amount of work done to break a big water drop of radius ' R ' into 27 small drops of equal radius is 10 J . The work done required to break the same big drop into 64 small drops of equal radius will be :-

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  8. Question 8

    2 Apr 2025

    79
    Two water drops each of radius ' rr ' coalesce to form a bigger drop. If ' T ' is the surface tension, the surface energy released in this process is :

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  9. Question 9

    2 Apr 2026 S1

    20
    A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is α×10−6 J\alpha \times10^{- 6}\text{ }J. The value of α\alpha is ____\_\_\_\_ . (Take surface tension of liquid =0.08 N/m= 0.08\text{ }N/m )

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  10. Question 10

    5 Apr 2026 S2

    8
    Eight mercury drops, each of radius rr, coalesce to form a bigger drop. The surface energy released in this process is ____\_\_\_\_ . (S is the surface tension of mercury).

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