The amount of work done in blowing a sops bubble such that its diameter increases from ' $d$ ' to…
The amount of work done in blowing a sops bubble such that its diameter increases from ' $d$ ' to $\mathrm{D}$ ' is ( $\mathrm{T}$ = surface tension of solution )
$4 \pi\left(D^2-d^2\right) T$
$8 \pi\left(D^2-d^2\right) T$
$\pi\left(D^2-d^2\right) T$
$2 \pi\left(D^2-d^2\right) T$
Solution
Change in surface area
$\begin{aligned} & =2 \times 4 \pi\left[\left(\frac{\mathrm{D}}{2}\right)^2-\left(\frac{\mathrm{d}}{2}\right)^2\right]=2 \pi\left(\mathrm{D}^2-\mathrm{d}^2\right) \\ & \therefore \text { Work done }=\text { surface tension } \times \text { change in area } \\ & =2 \pi\left(\mathrm{D}^2-\mathrm{d}^2\right) \mathrm{T}\end{aligned}$