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

The correct option is 8TL.

Let's understand the physics behind this step-by-step:

1. When a square frame of side $L$ is dipped into a liquid and taken out, a thin liquid membrane (or film) is formed within the frame.

2. A liquid membrane in the air always has two free surfaces in contact with the air (one on the front side and one on the back side).

3. The surface tension $T$ acts along the entire boundary (perimeter) of the frame for both of these free surfaces. Thus, the effective length of contact with the liquid film is twice the perimeter of the square frame.

4. The perimeter of a square frame of side $L$ is given by:
$\mathrm{Perimeter}=4L$

5. Since there are two free surfaces, the total contact length $L_{\mathrm{eff}}$ is:
$L_{\mathrm{eff}}=2\times 4L=8L$

6. The force $F$ due to surface tension is defined as the surface tension $T$ multiplied by the effective length of contact:
$F=T\times L_{\mathrm{eff}}$

7. Substituting the value of $L_{\mathrm{eff}}$ into the equation, we get:
$F=T\times 8L=8TL$

Therefore, the force acting on the frame is 8TL.