Two soap bubbles of radii 2 cm and 3 cm are brought in contact. Find the radius of curvature (in cm) of the contact surface.

Answer

To find the radius of curvature of the contact surface between two soap bubbles with radii of 2 cm and 3 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Radii of the Bubbles:**
- Let the radius of the smaller bubble (R1) be 2 cm.
- Let the radius of the larger bubble (R2) be 3 cm.

2. **Understanding the Concept of Radius of Curvature:**
- When two bubbles come into contact, the radius of curvature (R) of the contact surface can be calculated using the formula:
\[ \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \]
- Here, R1 and R2 are the radii of the two bubbles.

3. **Substituting the Values:**
- Substitute R1 = 2 cm and R2 = 3 cm into the formula:
\[ \frac{1}{R} = \frac{1}{2} + \frac{1}{3} \]

4. **Finding a Common Denominator:**
- The common denominator for 2 and 3 is 6. Thus, we can rewrite the fractions:
\[ \frac{1}{R} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \]

5. **Calculating R:**
- Now, take the reciprocal to find R:
\[ R = \frac{6}{5} \text{ cm} = 1.2 \text{ cm} \]

### Final Answer:
The radius of curvature of the contact surface is **1.2 cm**.