Question

The potential energy possessed by a soap bubble, having surface tension equal to $0.04 \,N/m$ of diameter $1\, cm$ is

• A. $6 \pi \times 10^{-6} J$
• B. $2 \pi \times 10^{-6} J$
• C. $8 \pi \times 10^{-6} J$
• D. $4\pi \times 10^{-6} J$

Answer 1

Answer: (C)

Given: Surface tension in soap bubble $(T)$ $=0.04\, N / m$ and diameter of soap bubble $(d)=1\, cm$ $=0.01\, m$ or radius $(r)=0.005 \,m$.
We know that potential energy $=$ Surface tension $\times$ Surface area.
We also know that for a soap bubble, there are two surfaces.
Therefore total area $=2 \times 4 \pi r^{2} .$
Thus potential energy $=(0.04) \times\left[2 \times 4 \pi \times(0.005)^{2}\right]=8 \pi \times 10^{-6}\, J .$