The work done in blowing a soap bubble of volume ' $\mathrm{V}$ ' is ' $\mathrm{W}$ '. The work required to…

The work done in blowing a soap bubble of volume ' $\mathrm{V}$ ' is ' $\mathrm{W}$ '. The work required to blow a soap bubble of volume ' $2 \mathrm{~V}$ ' is [ $\mathrm{T}=$ surface tension of soap solution $]$
  1. $2^{2 / 3} \mathrm{~W}$
  2. 2W
  3. W
  4. $2^{1 / 2} \mathrm{~W}$

Solution

$\begin{aligned} & \mathrm{V}=\frac{4}{3} \pi \mathrm{r}^3 \text { or } \quad \mathrm{r}=\left(\frac{3 \mathrm{~V}}{4 \pi}\right)^{1 / 3} \\ & \mathrm{~W}=8 \pi \mathrm{r}^2 \mathrm{~T}=8 \pi\left(\frac{3 \mathrm{~V}}{4 \pi}\right)^{2 / 3} \mathrm{~T} \\ & \mathrm{~W} \propto \mathrm{V}^{2 / 3} \\ & \frac{\mathrm{W}^{\prime}}{\mathrm{W}}=\left(\frac{2 \mathrm{~V}}{\mathrm{~V}}\right)^{2 / 3}=2^{2 / 3}\end{aligned}$

Asked in: MHT CET 2021 (23 Sep Shift 1)

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