Question:
A soap bubble of radius \(\frac{1}{\sqrt{π}}\) cm is expanded to radius \(\frac{3}{\sqrt{π}}\) cm. Surface tension of soap solution is 25 dyne/cm. The work done during expansion in erg is
A soap bubble of radius \(\frac{1}{\sqrt{π}}\) cm is expanded to radius \(\frac{3}{\sqrt{π}}\) cm. Surface tension of soap solution is 25 dyne/cm. The work done during expansion in erg is
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A soap bubble has two surfaces, so \(W=T\times2\times\Delta A\).
Updated On: Oct 1, 2026
- \(800\)
- \(1200\)
- \(1600\)
- \(2400\)
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
A soap bubble has an inner and an outer surface. The work done equals surface tension times the increase in total surface area.
Step 2: Key Formula or Approach
\[ W=T\cdot2\cdot4\pi\left(r_2^2-r_1^2\right) \]
Step 3: Detailed Explanation
\(r_1^2=\dfrac1\pi\) cm\(^2\) and \(r_2^2=\dfrac9\pi\) cm\(^2\).
\[ W=25\times2\times4\pi\times\frac{8}{\pi}=25\times64=1600\ \text{erg} \]
Final Answer:
The work done is 1600 erg, option (C). \[ \boxed{1600\ \text{erg (C)}} \]
A soap bubble has an inner and an outer surface. The work done equals surface tension times the increase in total surface area.
Step 2: Key Formula or Approach
\[ W=T\cdot2\cdot4\pi\left(r_2^2-r_1^2\right) \]
Step 3: Detailed Explanation
\(r_1^2=\dfrac1\pi\) cm\(^2\) and \(r_2^2=\dfrac9\pi\) cm\(^2\).
\[ W=25\times2\times4\pi\times\frac{8}{\pi}=25\times64=1600\ \text{erg} \]
Final Answer:
The work done is 1600 erg, option (C). \[ \boxed{1600\ \text{erg (C)}} \]
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