Question

If \(450\) erg of work is done in blowing a soap bubble of radius '\(r\)', the additional work required to be done to blow it to a radius equal to \(3r\) is

• A. \(2400\) erg
• B. \(3000\) erg
• C. \(3600\) erg
• D. \(4000\) erg

Hint:

A soap bubble has two surfaces, so work is T times 2 times 4 pi r squared; work scales as r squared.

Answer 1

The Correct Option is C

Step 1: Compare areas:
Total surface area (two surfaces) goes from $8\pi r^2$ to $8\pi(3r)^2 = 72\pi r^2$. The increase is $64\pi r^2$.

Step 2: Ratio of increase to the original area:
$\frac{64\pi r^2}{8\pi r^2} = 8$.

Step 3: Work:
Additional work $= 8 \times 450 = 3600$ erg.

Final Answer:
The additional work is 3600 erg, option (C). \[ \boxed{3600\text{ erg}} \]