Question

A film of water is formed between two straight parallel wires each $10\text{cm}$ long and at separation $0.5\text{cm}$. Calculate the work required to increase $1\text{mm}$ distance between the wires. Surface tension of water$=72\times {10}^{-3}\text{N/m}$.

• A. $144\times {10}^{-7}\text{J}$
• B. $104\times {10}^{-7}\text{J}$
• C. $72\times {10}^{-7}\text{J}$
• D. $288\times {10}^{-7}\text{J}$

Answer 1

The correct option is A $144\times {10}^{-7}\text{J}$

Given:
As film has two layer.
Initial surface area$=2\times (\text{length of wires}\times \text{separation between them)}$
$=2\times 10\text{cm}\times 0.5\text{cm}$
$=10\times {10}^{-4}{\text{m}}^2$
Final surface area$=2\times (\text{length of wires}\times \text{separation between them)}$
$=2\times 10\text{cm}\times (0.5+0.1)\text{cm}$
$=12\times {10}^{-4}{\text{m}}^2$

The required work,
$W=T\Delta A$
$=72\times {10}^{-3}\times (12\times {10}^{-4}-10\times {10}^{-4})\text{J}$
$=144\times {10}^{-7}\text{J}$