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  4. A square wire frame of size L is dipped in a liquid. On taking out, a membrane is formed. If the surface tension of liquid is T, the force acting on the frame will be :

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Q. A square wire frame of size $L$ is dipped in a liquid. On taking out, a membrane is formed. If the surface tension of liquid is $T$, the force acting on the frame will be :

Delhi UMET/DPMTDelhi UMET/DPMT 2004Mechanical Properties of Fluids

Solution:

The surface tension of a liquid is defined as the force per unit length in the plane of the liquid surface, acting at right angles on either side of an imaginary line drawn on that surface. Thus,
Since, membrane has two free surfaces,
total force acting is given by
$ F=2\times T\times $ boundary of frame
$ F= 2T\times4L $
$F=8\,TL$