If the work done in blowing a soap bubble of | vedclass

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(B) The volume of a spherical soap bubble is given by $V = \frac{4}{3} \pi r^3$,which implies $V \propto r^3$ or $r \propto V^{1/3}$.For a soap bubble

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$4^{1/3}W$

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(B) The volume of a spherical soap bubble is given by $V = \frac{4}{3} \pi r^3$,which implies $V \propto r^3$ or $r \propto V^{1/3}$.For a soap bubble,the work done $W$ in blowing it to a radius $r$ is $W = T 	imes \Delta A$,where $\Delta A = 2 	imes (4 \pi r^2) = 8 \pi r^2$ (since a soap bubble has two surfaces).Therefore,$W \propto r^2$.Substituting $r \propto V^{1/3}$,we get $W \propto (V^{1/3})^2 = V^{2/3}$.Let $W_1 = W$ for volume $V_1 = V$,and $W_2$ be the work for volume $V_2 = 2V$.Then,$\frac{W_2}{W_1} = \left( \frac{V_2}{V_1} ight)^{2/3} = (2)^{2/3} = (2^2)^{1/3} = 4^{1/3}$.Thus,$W_2 = 4^{1/3}W$.

If the work done in blowing a soap bubble of volume $V$ is $W$,then the work done in blowing a soap bubble of volume $2V$ will be

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