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 ' 2 V ' will be

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Aicharya · Accepted Answer

The work done is given as $\mathrm{W}=\mathrm{T} \Delta \mathrm{A}$ Volume of sphere is $V=\frac{4}{3} \pi \mathrm{r}^3$ Area of sphere is $\mathrm{A}=4 \pi \mathrm{r}^2$ $\begin{array}{ll} 	herefore & \mathrm{A} \propto \mathrm{~V}^{\frac{2}{3}} \ 	herefore & \mathrm{~W} \propto \mathrm{~V}^{\frac{2}{3}} \end{array}$ $\begin{aligned} & \frac{\mathrm{W}^{\prime}}{\mathrm{W}}=\frac{\mathrm{V}^{\frac{2}{3}}}{\mathrm{~V}^{\frac{2}{3}}} \ & \frac{\mathrm{~W}^{\prime}}{\mathrm{W}}=\frac{(2 \mathrm{~V})^{\frac{2}{3}}}{\mathrm{~V}^{\frac{2}{3}}} \ 	herefore \quad \frac{\mathrm{~W}^{\prime}}{\mathrm{W}} & =2^{\frac{2}{3}}=4^{\frac{1}{3}} \ 	herefore \quad \mathrm{~W}^{\prime} & =4^{\frac{1}{3}} \mathrm{~W}\end{aligned}$ $\ldots(\because \mathrm{V}=2 \mathrm{~V})$

If the work done in blowing a soap bubble of volume ' V ' is ' W ', then the work done in blowing a soap…

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