Question

If work done in blowing a soap bubble of radius 'R' is W. Then work done in blowing a soap bubble of radius 4R will be :-

• A. $2W$
• B. $4W$
• C. $8W$
• D. $16W$

Answer 1

The correct option is D $16W$

Let surface tension on the surface of the soap bubble $=$T

Total surface area of the soap bubble $=2\left(4\pi R^2\right)$

$=8\pi R^2$ (As the soap bubble has inner as well as outer surface)

Work done in blowing soap bubble $=$ Surface tension $\times$ Charge in area

$\Rightarrow W=8\pi R^{2}T\to \left(1\right)$

Now when radius becomes $4R$,

Work done $=8\pi \left(4R^2\right)T=16\times 8\pi R^{2}T=16W$.(Using $1$)