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Surface energy ratio when 1000 small drops combine into one big drop

The same question, asked 4 times: 25 Jan 2023, 30 Jan 2024, 1 Feb 2024, 6 Apr 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    25 Jan 2023

    112
    A spherical drop of liquid splits into 1000 identical spherical drops. If uiu_{i} is the surface energy of the original drop and ufu_{f} is the total surface energy of the resulting drops, the (ignoring evaporation), ufui=\frac{u_{f}}{u_{i}}= (10x)\left( \frac{10}{x} \right). Then value of xx is_____

  2. Question 2

    30 Jan 2024

    112
    A big drop is formed by coalescing 1000 small identical drops of water. If E1E_{1} be the total surface energy of 1000 small drops of water and E2E_{2} be the surface energy of single big drop of water, the E1E_{1} : E2E_{2} is x:1x:1 where x=x = _______

  3. Question 3

    1 Feb 2024

    97
    A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become:

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  4. Question 4

    6 Apr 2024

    23
    A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is 10x\frac{10}{x}. The value of xx is_____________.