Question

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

Answer 1

Here, In the question we can see the distance between the parallel wire is changing, so work done required to increase the distance between the wires by $1\,mm$ can be found by multiplying surface tension and change in area.

Complete answer:

Here the increase in area is shown by shaded portion in the figure since this is a water film it has two surface therefore increase in area,
$\Delta S = 2\, \times \,10\, \times \,0.1\, = \,2c{m^2}$(Since,1\,mm$$$$ = 0.1cm)
Therefore, work required to be done is,
$W = \Delta S\, \times \,T$(Where$\Delta S$ is change in area and $T$ is the Surface Tension)
On putting the values of $\Delta S$& $T$ we get,

$$\Rightarrow 2 \times {10^{ - 4}} \times 72 \times {10^{ - 3}} \\\ \Rightarrow 144 \times {10^{ - 7}}\,Joule \\\ \Rightarrow 1.44 \times {10^{ - 5}}\,Joule \\\$$

Hence, the work done required to increase $1\,mm$ separation will be $1.44 \times {10^{ - 5}}\,Joule$

Additional information:
Surface tension could be defined as the property of the surface of a liquid that allows it to resist an external force, due to the cohesive nature of the water molecules.

Note:
This type of question can be done by simple calculations and if we know the concept of liquid mechanics and their formula. As we can see, here in this question the concept of surface tension is used and the work done required to increase the separation between two wires having water film formed.