Work done in increasing the size of a soap bubble from radius of $3 \mathrm{~cm}$ to $5 \mathrm{~cm}$ in…

Work done in increasing the size of a soap bubble from radius of $3 \mathrm{~cm}$ to $5 \mathrm{~cm}$ in millijoule is nearly (surface tension of soap solution $=0.03 \mathrm{Nm}^{-1}$ )
  1. $0.4 \pi$
  2. $0.2 \pi$
  3. $4 \pi$
  4. $2 \pi$

Solution

$\begin{aligned} & \mathrm{w}=8 \pi \mathrm{T}\left(\mathrm{r}_2^2-\mathrm{r}_1^2\right) \\ & =8 \pi \times 0.03(25-9) \times 10^{-4} \\ & =0.384 \pi \times 10^{-3} \mathrm{~J} \\ & =0.384 \pi \mathrm{mJ} \approx 0.4 \pi \mathrm{mJ}\end{aligned}$

Asked in: MHT CET 2021 (23 Sep Shift 2)

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