Question

The work done in blowing a soap bubble of radius \( R \) is \( W \). The work done in blowing a bubble of radius \( 2R \) of the same soap solution is

• A. \( \frac{W}{4} \)
• B. \( \frac{W}{2} \)
• C. \( 4W \)
• D. \( 2W \)

Hint:

The work done in blowing a soap bubble increases with the square of the radius because the surface area increases with the square of the radius.

Answer 1

The Correct Option is C

Step 1: Understanding the work done in blowing a soap bubble.
The work done to blow a soap bubble is proportional to the surface area of the bubble. The surface area of a bubble is given by \( A = 4\pi r^2 \), where \( r \) is the radius of the bubble.
Step 2: Surface area comparison.
For a bubble of radius \( R \), the surface area is \( A_1 = 4\pi R^2 \). For a bubble of radius \( 2R \), the surface area is \( A_2 = 4\pi (2R)^2 = 16\pi R^2 \).
Step 3: Work comparison.
Since work is proportional to surface area, the work done in blowing the bubble with radius \( 2R \) is: \[ W_2 = 4 \times W_1 = 4W \]
Step 4: Conclusion.
The work done in blowing a bubble of radius \( 2R \) is \( 4W \), so the correct answer is (C) \( 4W \).