Question

A thin liquid film formed between a $U$ - shaped wire and supports a light weight of $1.5\times {10}^{-2}\text{N}$ (see figure). The length of the slider is $30\text{cm}$ and its weight is negligible. The surface tension of the liquid film is

• A. $0.0125{\text{Nm}}^{-1}$
• B. $0.1{\text{Nm}}^{-1}$
• C. $0.05{\text{Nm}}^{-1}$
• D. $0.025{\text{Nm}}^{-1}$

Answer 1

The correct option is D $0.025{\text{Nm}}^{-1}$

Here, $W=1.5\times {10}^{-2}\text{N}$
$L=30\text{cm}=30\times {10}^{-2}\text{m}$
As film has two surface.
$\therefore \text{Force due surface tension}=2\times L\times S$

At equilibrium, weight of the give block is balanced by force due to surface tension, i.e.,
$2L\times S=W$
$\Rightarrow S=\frac{W}{2L}=\frac{1.5\times {10}^{-2}\text{N}}{2\times 0.3\text{m}}=0.025\text{N/m}$