There are two thin films A of liquid and B of polythene, identical in size they are being pulled with same maximum weight W. if the breadth of the films is increased from b to 2 b then the corresponding weights will be respectively

Options

A. W,W
B. `(W)/(2),(W)/(2)`
C. `(W)/(2),W`
D. `W,(W)/(2)`

Answer

To solve the problem, we need to analyze the forces acting on the two thin films, A (liquid) and B (polythene), when they are subjected to a pulling force.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two thin films: Film A (liquid) and Film B (polythene).
- Both films are identical in size and are being pulled with the same maximum weight \( W \).

2. **Effect of Breadth Increase**:
- The breadth of both films is increased from \( b \) to \( 2b \).
- This increase in breadth affects the surface area of the films.

3. **Surface Energy Consideration**:
- For Film A (liquid), it has two free surfaces. The force acting on it is due to the surface tension acting on both surfaces.
- For Film B (polythene), it has only one free surface, so the force acting on it is due to the surface tension acting on one surface.

4. **Weight Relations**:
- Let \( W_L \) be the weight corresponding to Film A (liquid) and \( W_P \) be the weight corresponding to Film B (polythene).
- The relationship between the weights can be established as:
\[ W_P = \frac{1}{2} W_L \]
- This is because the liquid film has two surfaces contributing to the force, while the polythene film has only one.

5. **Substituting Maximum Weight**:
- According to the problem, the maximum weight applied to both films is \( W \).
- Therefore, we can set:
\[ W_L = W \quad \text{(for the liquid film)} \]
\[ W_P = \frac{1}{2} W_L = \frac{1}{2} W \quad \text{(for the polythene film)} \]

6. **Final Result**:
- The corresponding weights after increasing the breadth are:
- For Film A (liquid): \( W_L = W \)
- For Film B (polythene): \( W_P = \frac{W}{2} \)

### Conclusion:
The corresponding weights for the films after the breadth increase are:
- Film A (liquid): \( W \)
- Film B (polythene): \( \frac{W}{2} \)