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 $30cm$. What is the surface tension of the film?

• A. $3\times {10}^{-3}N{m}^{-1}$
• B. $2\times {10}^{-5}N{m}^{-1}$
• C. $4\times {10}^{-4}N{m}^{-1}$
• D. $2.5\times {10}^{-2}N{m}^{-1}$

Answer 1

Answer: (D)

$2.5\times {10}^{-2}N{m}^{-1}$

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., $f=w=mg$
$T\times 0.6=1.5\times {10}^{-2}$
$T=\frac{1.5\times {10}^{-2}}{0.6}$
$T=2.5\times {10}^{-2}N{m}^{-1}$