Question

A film of water is formed between two straight parallel wires each 10 cm long and at a separation of $0.5cm$. Calculate the work required to increase the distance between them by $1mm$. The surface tension of water =$72×{10}^{-30}N/m$

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Solution

Step 1:Given data:Length of wires =$10cm=0.1m$Separation between wires=$0.5cm=5×{10}^{-3}m$Distance to be increased between wires=1mm=$1×{10}^{-3}$mThe surface tension of water=$72×{10}^{-30}N/m$Change in surface area = $\Delta S$Surface Tension = $T$Step 2: Formulae usedChange in surface area=Area of films $×$no.of filmsWork done=$\Delta S×T$Step 3:SolutionWork done by water to increase the separation= Change in surface area $×$Surface Tension Change in surface area=$\Delta$S=Area of films $×$no.of films $=0.1×1×{10}^{-3}×2\phantom{\rule{0ex}{0ex}}=2×{10}^{-4}$( Water has 2 films ) Work done=$\Delta$$S$$×T$ =$=2×{10}^{-3}×72×{10}^{-30}\phantom{\rule{0ex}{0ex}}=144×{10}^{-7}J\phantom{\rule{0ex}{0ex}}=1.44×{10}^{-2}J$So, Work done to increase the separation between 2 parallel wires by $1mm$ is equal to $1.44×{10}^{-2}J$

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