A circular wire, 10 cm in diameter, with a slider wire on it, is in a horizontal plane. A liquid film is formed, bounded by the wires, on the left side of the slider, as shown. The surface tension of the liquid is 0.1 N/m. An applied force 16 mN, perpendicular to the slider, maintains the film in equilibrium. Ignore the sag in the film. What can be the distance between point P and slider

Given Data

• Diameter of circular wire = 10 cm = 0.1 m
• Surface tension (T) = 0.1 N/m
• Applied force (F) = 16 mN = 0.016 N
• Slider wire moves perpendicularly to the applied force, maintaining film equilibrium
• Sag in the film is ignored

Step-by-Step Solution

Step 1: Principle

The force necessary to balance the surface tension acts along both edges of the liquid film. Thus, the total length affected by surface tension is twice the length between point P and the slider (since the film has two surfaces).

Let the distance between point P and the slider be L.

Step 2: Force Due to Surface Tension

Surface tension force on both sides is:

F_T = 2 × T × L

Step 3: Equilibrium Condition

Applied force F is balanced by surface tension force:

F = 2T · L

Substitute given values:

0.016 = 2 × 0.1 × L

Step 4: Solve for L

0.016 = 0.2 × L

L = ^0.016⁄_0.2

L = 0.08 m

L = 8 cm

Final Answer

The distance between point P and the slider should be 8 cm.