Blowing a soap bubble of volume V requires work W. How much work is needed to blow a soap bubble of volume 2V (same liquid)?

W
2^(2/3) W
2^(1/3) W
2W

Correct answer: 2^(2/3) W

Solution

Since W is proportional to surface area (proportional to r²) and V is proportional to r³, doubling V multiplies r by 2^(1/3) and area by (2^(1/3))² = 2^(2/3).

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