The work done in increasing the size of a soap film from 10cm x 6cm to 10cm x 11cm is 3 x 10⁻⁴ J. The surface tension of the film is

The correct option is 3.0 x 10⁻² Nm⁻¹.

Step-by-Step Explanation:

1. Understand the Formula for Work Done in a Soap Film:
A soap film has two free surfaces in contact with the air. When the surface area of a soap film is increased, work is done against the surface tension force on both sides. Therefore, the work done ($W$) is given by the formula:
$W=2\cdot T\cdot \mathrm{\Delta A}$
where:
• $T$ is the surface tension of the soap solution,
• $\mathrm{\Delta A}$ is the change in area of one side of the film, and
• the factor of 2 accounts for the two surfaces of the soap film.

2. Calculate the Change in Area ($\mathrm{\Delta A}$):
The initial dimensions of the film are $10\text{cm}\times 6\text{cm}$.
Initial Area, $A_1=10\text{cm}\times 6\text{cm}=60{\text{cm}}^2=60\times {10}^{-4}{\text{m}}^2$.
The final dimensions of the film are $10\text{cm}\times 11\text{cm}$.
Final Area, $A_2=10\text{cm}\times 11\text{cm}=110{\text{cm}}^2=110\times {10}^{-4}{\text{m}}^2$.
Therefore, the change in area is:
$\mathrm{\Delta A}=A_2-A_1=(110-60){\text{cm}}^2=50{\text{cm}}^2=50\times {10}^{-4}{\text{m}}^2$.

3. Calculate the Surface Tension ($T$):
We are given the work done, $W=3\times {10}^{-4}\text{J}$.
Substitute the values of $W$ and $\mathrm{\Delta A}$ into the work formula:
$3\times {10}^{-4}=2\cdot T\cdot (50\times {10}^{-4})$
$3\times {10}^{-4}=100\times {10}^{-4}\cdot T$
$3\times {10}^{-4}={10}^{-2}\cdot T$
Solving for $T$:
$T=\frac{3\times {10}^{-4}}{{10}^{-2}}=3.0\times {10}^{-2}{\text{Nm}}^{-1}$

Thus, the surface tension of the soap film is $3.0\times {10}^{-2}{\text{Nm}}^{-1}$.