Two spherical soap bubbles of diameters 10 cm and 6 cm are formed, one at each end of a narrow horizontal glass tube. If the surface tension of the soap solution is `0.03 Nm^(-1)`, then the pressure difference in pascal between the two ends of the tube is

Options

A. 16
B. 1.6
C. 0.016
D. 0.08

Explanation

To find the pressure difference between the two ends of the tube due to the soap bubbles, we can use the formula for the pressure difference across a soap bubble, which is given by:

\[ \Delta P = \frac{4 \sigma}{R} \]

where:
- \(\Delta P\) is the pressure difference,
- \(\sigma\) is the surface tension of the soap solution,
- \(R\) is the radius of the bubble.

### Step 1: Calculate the radii of the bubbles
The diameters of the bubbles are given as:
- Diameter of bubble 1 (\(D_1\)) = 10 cm = 0.10 m
- Diameter of bubble 2 (\(D_2\)) = 6 cm = 0.06 m

Now, we can find the radii:
- Radius of bubble 1 (\(R_1\)) = \(\frac{D_1}{2} = \frac{0.10}{2} = 0.05\) m
- Radius of bubble 2 (\(R_2\)) = \(\frac{D_2}{2} = \frac{0.06}{2} = 0.03\) m

### Step 2: Calculate the pressure inside each bubble
Using the formula for pressure difference:
1. For bubble 1:
\[ \Delta P_1 = \frac{4 \sigma}{R_1} = \frac{4 \times 0.03}{0.05} \]
\[ \Delta P_1 = \frac{0.12}{0.05} = 2.4 \text{ Pa} \]

2. For bubble 2:
\[ \Delta P_2 = \frac{4 \sigma}{R_2} = \frac{4 \times 0.03}{0.03} \]
\[ \Delta P_2 = \frac{0.12}{0.03} = 4.0 \text{ Pa} \]

### Step 3: Calculate the pressure difference between the two bubbles
The pressure difference between the two ends of the tube is given by:
\[ \Delta P = \Delta P_2 - \Delta P_1 \]
Substituting the values we calculated:
\[ \Delta P = 4.0 \text{ Pa} - 2.4 \text{ Pa} = 1.6 \text{ Pa} \]

### Final Answer
The pressure difference between the two ends of the tube is:
\[ \Delta P = 1.6 \text{ Pa} \]