Question

Find the work done in increasing the volume of a soap bubble by $700 \%$ if its radius is $R$ and surface tension is $T$.

• A. $24 \pi R ^{2} T$
• B. $12 \pi R ^{2} T$
• C. $6 \pi R ^{2} T$
• D. $\pi R ^{2} T$

Answer 1

Answer: (A)

W.D. $=2 \times 4 \pi T \left( r _{2}^{2}- r _{1}^{2}\right)$
If initial volume $= V$
then final volume $=8 \,V$ then radius will become $2 R$
So W.D. $=2 \times 4 \pi T \left((2 R )^{2}- R ^{2}\right)$
$=24 \pi R ^{2} T$