Question

A soap bubble of radius \( r_1 \) is placed on another soap bubble of radius \( r_2 \) (\( r_1<r_2 \)). The radius \( R \) of the soapy film separating the two bubbles is

• A. \( r_2 + r_1 \)
• B. \( \frac{r_2 - r_1}{2} \)
• C. \( \frac{r_1}{2} \)
• D. \( \sqrt{r_1^2 + r_2^2} \)

Hint:

The film separating two soap bubbles has a radius equal to the sum of the radii of the bubbles due to the pressure difference.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
In the case of two soap bubbles, the film separating the bubbles will have a radius equal to the sum of the radii of the two bubbles because of the pressure difference between the inside and outside of the bubbles.

Step 2: Applying the principle.
The pressure difference between the two soap films results in the separation distance being the sum of their radii. Thus, the radius of the film separating the bubbles is \( r_2 + r_1 \).