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Q.

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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a

2 W

b

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

c

$\sqrt{2} W$

d

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

answer is D.

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Detailed Solution

$W = 4 {πr}^{2} σ . Now V = \frac{4}{3} {πr}^{3} . Hence W = 4 πσ {(\frac{3 V}{4 π})}^{2 / 3}, i . e . W \propto V^{2 / 3}$

Hence the correct choice is ( 4).

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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?