Question

A water film is formed between two straight parallel wires, each of length \(10\,\text{cm}\), kept at a separation of \(0.5\,\text{cm}\). Now, the separation between them is increased by \(1\,\text{mm}\) without breaking the water film. The work done for this is (surface tension of water \(= 7.2 \times 10^{-2}\,\text{N m}^{-1}\))

• A. \(7.22 \times 10^{-6}\,\text{J}\)
• B. \(5.76 \times 10^{-5}\,\text{J}\)
• C. \(1.44 \times 10^{-5}\,\text{J}\)
• D. \(2.88 \times 10^{-5}\,\text{J}\)

Hint:

Always multiply surface tension by 2 for a liquid film because it has two surfaces.

Answer 1

The Correct Option is C

Step 1: Force due to surface tension.
For a water film, force due to surface tension on each wire is \[ F = 2Tl, \] where \(l = 0.10\,\text{m}\).
Step 2: Work done.
Work done in increasing separation by \(\Delta x\) is \[ W = F \Delta x = 2Tl\Delta x. \]
Step 3: Substitution.
\[ W = 2 \times 7.2\times10^{-2} \times 0.10 \times 1\times10^{-3} = 1.44\times10^{-5}\,\text{J}. \]
Step 4: Conclusion.
The work done is \(1.44 \times 10^{-5}\,\text{J}\).