If the excess pressure inside a soap bubble is balanced by oil column of height 2 mm, then the surface tension of soap solution will be
`(r = 1` cm and density `d g = 10 ms^(-2) = 0.8 g c c^(-1))`.

Options

A. `4 N m^(-1)`
B. ` 4 xx 10 N m^(-1)`
C. `4 xx 10^(-2) Nm^(-1)`
D. `4 xx 10^(-3) Nm^(-1)`

Answer

To solve the problem, we need to find the surface tension of the soap solution given that the excess pressure inside the soap bubble is balanced by an oil column of height 2 mm.

### Step-by-Step Solution:

1. **Understand the Concept of Excess Pressure**:
The excess pressure inside a soap bubble is given by the formula:
\[ \Delta P = \frac{4S}{R} \]
where \( S \) is the surface tension and \( R \) is the radius of the bubble.

2. **Convert Given Values**:
- The radius \( R \) is given as 1 cm, which we convert to meters:
\[ R = 1 \text{ cm} = 0.01 \text{ m} \]
- The height of the oil column \( h \) is given as 2 mm, which we convert to meters:
\[ h = 2 \text{ mm} = 0.002 \text{ m} \]
- The density \( d \) of the oil is given as \( 0.8 \text{ g/cm}^3 \). We convert this to \( \text{kg/m}^3 \):
\[ d = 0.8 \text{ g/cm}^3 = 0.8 \times 1000 \text{ kg/m}^3 = 800 \text{ kg/m}^3 \]

3. **Calculate the Excess Pressure from the Oil Column**:
The excess pressure due to the oil column is given by:
\[ \Delta P = \rho g h \]
where \( \rho \) is the density of the oil, \( g \) is the acceleration due to gravity, and \( h \) is the height of the oil column.
Substituting the values:
\[ \Delta P = 800 \text{ kg/m}^3 \times 10 \text{ m/s}^2 \times 0.002 \text{ m} \]
\[ \Delta P = 800 \times 10 \times 0.002 = 16 \text{ N/m}^2 \]

4. **Substitute into the Excess Pressure Formula**:
Now we substitute \( \Delta P \) back into the excess pressure formula for the soap bubble:
\[ 16 = \frac{4S}{0.01} \]

5. **Solve for Surface Tension \( S \)**:
Rearranging the equation to solve for \( S \):
\[ S = \frac{16 \times 0.01}{4} \]
\[ S = \frac{0.16}{4} = 0.04 \text{ N/m} \]

6. **Final Result**:
Thus, the surface tension of the soap solution is:
\[ S = 4 \times 10^{-2} \text{ N/m} \]