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

Options

A. 2 T L
B. 4 T L
C. 8 T L
D. 10 T L

Explanation

To solve the problem, we need to determine the force acting on a square wire frame of size \( L \) when it is dipped in a liquid with surface tension \( T \). Here’s a step-by-step solution:

### Step 1: Understand the Geometry of the Frame
The wire frame is square with each side of length \( L \). Therefore, the perimeter of the square frame can be calculated as:
\[ \text{Perimeter} = 4L \]

### Step 2: Identify the Free Surfaces
When the square wire frame is dipped in the liquid and then taken out, a membrane is formed on the surface of the liquid. Since the frame has two free surfaces (the top and the bottom), we need to consider the effect of surface tension on both of these surfaces.

### Step 3: Calculate the Total Length Contributing to Surface Tension
Since there are two free surfaces, the effective length that contributes to the surface tension is:
\[ \text{Total Length} = 2 \times \text{Perimeter} = 2 \times 4L = 8L \]

### Step 4: Relate Surface Tension to Force
Surface tension \( T \) is defined as the force per unit length. Therefore, the total force \( F \) acting on the frame due to surface tension can be expressed as:
\[ F = T \times \text{Total Length} \]

### Step 5: Substitute the Values
Now, substituting the total length we calculated:
\[ F = T \times 8L \]

### Step 6: Final Expression for Force
Thus, the force acting on the frame is:
\[ F = 8TL \]

### Conclusion
The force acting on the square wire frame when it is taken out of the liquid is \( 8TL \).