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Radius of the bubble formed when two soap bubbles coalesce isothermally

The same question, asked 3 times: 9 May 2024 S1, 14 May 2024 S2, 26 Apr 2025 S2. Every wording below, oldest first.

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  1. Question 1

    9 May 2024 S1

    27
    The radii of two soap bubbles are r1r_1 & r2r_2. In isothermal condition they combine with each other to form a single bubble. The radius of resultant bubble is:

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  2. Question 2

    14 May 2024 S2

    22
    Two spherical soap bubbles of radii aa and bb in vacuum coalesce under isothermal conditions. The resulting bubble has a radius equal to

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  3. Question 3

    26 Apr 2025 S2

    23
    Under isothermal conditions, two soap bubbles of radii r1r_{1} and r2r_{2} coalesce to form a big drop. The radius of the big drop is

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