If a section of soap bubble (of radius R) through its centre is considered then force on one half due to surface thension is

Options

A. `2piRT`
B. `4piRT`
C. `piR^(2)T`
D. `(4T)/(R)`

Answer

To find the force on one half of a soap bubble due to surface tension, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Soap Bubble**: A soap bubble has two surfaces (inner and outer) and is spherical in shape with a radius \( R \).

2. **Surface Tension Concept**: Surface tension (\( T \)) is the force per unit length acting along the surface of the liquid. It acts tangentially to the surface.

3. **Cutting the Bubble**: When we consider a section of the soap bubble through its center, we can analyze the forces acting on one half of the bubble.

4. **Length Calculation**: The effective length over which the surface tension acts on one half of the bubble is the circumference of the circle formed by the cut, multiplied by the number of surfaces. Since there are two surfaces (inner and outer), the effective length \( L \) is:
\[ L = 2 \pi R \times 2 = 4 \pi R \]

5. **Force Due to Surface Tension**: The force (\( F \)) due to surface tension is given by the formula:
\[ F = T \times L \]
Substituting the value of \( L \):
\[ F = T \times (4 \pi R) = 4 \pi R T \]

6. **Final Result**: Thus, the force on one half of the soap bubble due to surface tension is:
\[ F = 4 \pi R T \]

### Conclusion:
The force on one half of the soap bubble due to surface tension is \( 4 \pi R T \).

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