Multiple choice

The energy required to increase the radius of a bubble r to 2r is (surface tension of bubble is T)?

  1. 28πr2T

  2. 24πr2T

  3. 32πr2T

  4. 8πr2T
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work done = Surface Tension * Change in Surface Area. A bubble has two surfaces. Initial area = 2 * (4 * pi * r^2) = 8 * pi * r^2. Final area = 2 * (4 * pi * (2r)^2) = 32 * pi * r^2. Change in area = 24 * pi * r^2. Energy = T * 24 * pi * r^2.

AI explanation

A bubble has an outer and an inner surface, so its initial total surface area is 2 * 4 * pi * r^2 = 8 * pi * r^2. When the radius increases to 2r, the new total surface area becomes 2 * 4 * pi * (2r)^2 = 32 * pi * r^2. The change in surface area is 32 * pi * r^2 - 8 * pi * r^2 = 24 * pi * r^2, meaning the required energy is T * 24 * pi * r^2. The result is 24 * pi * r^2 * T.

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