The work done in increasing the size of a soap film from 10 cm × 6 cm to 10 cm × 11 cm is 3 × 10^-4 joule. The surface tension of the film is:

CONCEPT:

Surface Tension

Surface tension is a property of liquids that makes them acquire the least surface area possible. It is the force per unit length acting along the surface of a liquid.

The work done in increasing the surface area of a liquid film is given by the product of the surface tension and the change in surface area.

EXPLANATION:

Let's calculate the surface tension of the soap film:

The initial dimensions of the soap film are 10 cm × 6 cm. Hence, the initial area (A₁) is:

A₁ = 10 cm × 6 cm = 60 cm²

The final dimensions of the soap film are 10 cm × 11 cm. Hence, the final area (A₂) is:

A₂ = 10 cm × 11 cm = 110 cm²

The change in area (ΔA) is:

ΔA = A₂ - A₁ = 110 cm² - 60 cm² = 50 cm²

The work done (W) in increasing the size of the soap film is given as 3 × 10^-4 joule.

The surface tension (γ) is calculated using the formula:

W = γ × ΔA

Rearranging the formula for γ gives:

γ = W / ΔA

Substitute the values:

γ = (3 × 10^-4 joule) / (50 cm²)

Note: 1 cm² = 10^-4 m², so 50 cm² = 50 × 10^-4 m²

γ = (3 × 10^-4 joule) / (50 × 10^-4 m²)

γ = (3 / 50) N/m

γ = 0.06 N/m

Therefore, the correct answer is option 2: 3.0 × 10^-2 N/m.