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: Understanding the Concept:
Work done in blowing a bubble equals surface tension times the increase in surface area. A soap bubble has two surfaces, so \(W = T\times2\times4\pi r^2 = 8\pi r^2T\).

Step 2: Scaling:
\(W \propto r^2\). When the radius becomes \(3r\), the work becomes \(9\) times larger (starting from zero radius):
\[ W_2 = 9 \times 450 = 4050 \text{ erg} \]

Step 3: Additional work:
\[ W_2 - W_1 = 4050 - 450 = 3600 \text{ erg} \]

Step 4: Why the other options are wrong.
2400 erg would result from an area ratio of \(\frac{16}{3}\)-type slip. 3000 erg and 4000 erg do not match a factor of 8 times the first work (3600 = 8 x 450).

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