A square wire frame of L is dipped in a liquid, on taking out a membrane is formed. If the surface tension of liquid is T, force acting on the frame will be

Options

A. 2TL
B. 4TL
C. 8TL
D. 10TL

Explanation

To find the force acting on a square wire frame of length \( L \) that is dipped in a liquid and forms a membrane when taken out, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Surface Tension**:
Surface tension (\( T \)) is a force that acts along the surface of a liquid. It is defined as the force per unit length acting on the surface of the liquid.

2. **Identify the Frame's Configuration**:
The wire frame is square, meaning it has four sides, each of length \( L \). Therefore, the total length of the frame in contact with the liquid is \( 4L \).

3. **Calculate the Force on One Side**:
When the frame is removed from the liquid, a membrane is formed across each side of the frame. The force due to surface tension acting on one side of the frame can be calculated as:
\[ \text{Force on one side} = T \times L \]
where \( T \) is the surface tension.

4. **Calculate the Total Force on the Frame**:
Since the membrane acts on both sides of each side of the frame, we need to consider the force acting on both sides. Thus, the total force acting on the frame is:
\[ \text{Total Force} = 2 \times (\text{Force on one side}) = 2 \times (T \times L) \]
However, since there are four sides, we need to account for the total length of the frame:
\[ \text{Total Force} = T \times (4L) \times 2 \]

5. **Final Calculation**:
Therefore, the total force acting on the square wire frame is:
\[ F = 8TL \]

### Conclusion:
The force acting on the frame when it is taken out of the liquid is given by:
\[ F = 8TL \]