Question

The potential energy possessed by a soap bubble, having surface tension equal to $0.04N/m$ of diameter $1cm$ 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 $(T)$ $=0.04N/m$ and diameter of soap bubble $(d)=1cm$ $=0.01m$ or radius $(r)=0.005m$.
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 $=(0.04)\times \left[2\times 4\pi \times (0.005{)}^2\right]=8\pi \times 10^{-6}J.$