The Problem:
A soap film initially measures 10cm×6cm and is then increased to 10cm×12cm. The surface tension of the soap solution is given as 30×10-3 Nm-1. We need to calculate the work done in the process.

Understanding the Problem:
To solve this problem, we need to understand the concept of surface tension and work done. Surface tension is a property of liquids that allows them to resist an external force. It is defined as the force per unit length acting perpendicular to an imaginary line drawn on the surface of the liquid. Work done is the energy transferred by a force acting through a distance.

Formula:
The formula for work done is given by:
Work = Force × Distance

Solution:
To calculate the work done, we need to find the force and the distance.

Calculating the Initial Force:
The initial force is the force acting on the soap film when its dimensions are 10cm×6cm. The force can be calculated using the formula:
Force = Surface Tension × Perimeter

The perimeter of the soap film can be calculated by adding the lengths of all four sides. Therefore, the initial force is given by:
Force_initial = Surface Tension × (2 × length + 2 × width)

Calculating the Initial Distance:
The initial distance is the perimeter of the soap film when its dimensions are 10cm×6cm. Therefore, the initial distance is given by:
Distance_initial = 2 × length + 2 × width

Calculating the Final Force:
The final force is the force acting on the soap film when its dimensions are increased to 10cm×12cm. The final force can be calculated using the same formula as the initial force.

Calculating the Final Distance:
The final distance is the perimeter of the soap film when its dimensions are 10cm×12cm. Therefore, the final distance is given by:
Distance_final = 2 × length + 2 × width

Calculating the Work Done:
Now that we have the initial force, initial distance, final force, and final distance, we can calculate the work done using the formula:
Work = (Final Force - Initial Force) × (Final Distance - Initial Distance)

Plug in the values and calculate the work done.

Final Answer:
The work done in the process is the calculated value using the given formula and values.