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Question
Two soap bubbles have a radius in the ratio of 2:3. Compare the works done in blowing these bubbles.
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Solution
Given: r1 : r2 = 2 : 3
To find: W1 : W2
Formula: W = 2TdA
Calculation: From the formula,
Work done to blow both bubbles,
W1 = `2T(4pir_1^2)` and W2 = `2T(4pir_2^2)`
∴ `"W"_1/"W"_2 = (r_1/r_2)^2 = (2/3)^2`
∴ W1 : W2 = 4 : 9
The ratio of work done to blow the bubbles is 4:9.
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