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A U-shaped wire is dipped in a soap solution an removed thin soap film formed between the wire and a light slider supports a weight of $1.5 \times 10^{-2} \mathrm{~N}$ (which includes the small weight of the slider). The length of the slider is 30 $\mathrm{cm}$. What is the surface tension of the film?
Solution:
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Verified Answer
Since, soap film has two free surfaces, so total length of the film $=2 \ell=2 \times 30=60 \mathrm{~cm}=0.6 \mathrm{~m}$.
Total force on the slider due to surface tension,
$$
\mathrm{F}=\mathrm{S} \times 2 \ell=5 \times 0.6 \mathrm{~N}
$$
In equilibrium, $\mathrm{F}=\mathrm{mg}$
$$
\begin{aligned}
&\therefore \quad \mathrm{S} \times 0.6=1.5 \times 10^{-2} \\
&\therefore \quad \mathrm{S}=\frac{1.5 \times 10^{-2}}{0.6}=2.5 \times 10^{-2} \mathrm{Nm}^{-1}
\end{aligned}
$$
Total force on the slider due to surface tension,
$$
\mathrm{F}=\mathrm{S} \times 2 \ell=5 \times 0.6 \mathrm{~N}
$$
In equilibrium, $\mathrm{F}=\mathrm{mg}$
$$
\begin{aligned}
&\therefore \quad \mathrm{S} \times 0.6=1.5 \times 10^{-2} \\
&\therefore \quad \mathrm{S}=\frac{1.5 \times 10^{-2}}{0.6}=2.5 \times 10^{-2} \mathrm{Nm}^{-1}
\end{aligned}
$$
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