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  4. Surface tension of the liquid is S. Work done in increasing the radius of soap bubble from R to 3R at given temperature will be

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Q. Surface tension of the liquid is $S$. Work done in increasing the radius of soap bubble from $R$ to $3R$ at given temperature will be

UPSEEUPSEE 2016

Solution:

Given, surface tension of the liquid is $S$.
Work done in blowing a soap bubble. So as to increase its radius from $R_{1}=R$ to $R_{2}=3 R$ is given by
$W=S \cdot 8 \pi\left[R_{2}^{2}-R_{1}^{2}\right]$
where $S=$ surface tension
$W =S \cdot 8 \pi\left[(3 R)^{2}-(R)^{2}\right]$
$=S \cdot 8 \pi\left[9 R^{2}-R^{2}\right]$
$=S \cdot 8 \pi \cdot 8 R^{2}=64 \pi R^{2} S .$