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Work w is required to be done to form a spherical bubble of volume V from a given soap solution. How much work is needed to form a spherical bubble of volume 2V.

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$(2^{1 / 3}) w$

$(4^{1 / 3}) w$

$\sqrt{2 w}$

answer is D.

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Detailed Solution

$w = 8 π r^{2} T Now, v = \frac{4}{3} π r^{3} Hence, w = 8 πT {(\frac{3 v}{4 r})}^{2 / 3} \Rightarrow w \propto v^{2 / 3} w = 8 πT {(\frac{3 v}{4 r})}^{2 / 3} \Rightarrow w \propto v^{2 / 3}$

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