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Question

A $$U$$-shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and light slider supports a weight of $$1.5\times { 10 }^{ 2 }N$$. The length of the slider is $$30 cm$$. What is the surface tension of the film?


A
3×103Nm1
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B
2×105Nm1
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C
4×104Nm1
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D
2.5×102Nm1
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Solution

The correct option is B $$2.5\times { 10 }^{ -2 }N{ m }^{ -1 }$$
A soap film has two free surfaces, so total length of the film to be supported,
$$l=2\times 30cm=0.60m$$
Let $$T=$$ surface tension of the film.
If $$f=$$ total force on the slider due to surface tension,
then   $$f=T\times 2l=T\times 0.6N$$
          $$W=1.5\times { 10 }^{ -2 }N$$
In equilibrium position, the force $$f$$ on the slider due to surface tension must be balanced by the weight $$\left( w \right)$$ supported by the slider
i.e., $$ f=w=mg$$
$$T\times 0.6=1.5\times { 10 }^{ -2 }$$
$$T=\dfrac { 1.5\times { 10 }^{ -2 } }{ 0.6 }$$
$$ T=2.5\times { 10 }^{ -2 }N{ m }^{ -1 }$$

Physics

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