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MHT CET · Physics · Mechanical Properties of Fluids

The radius \(R\) of the soap bubble is doubled under isothermal condition. If \(T\) be the surface tension of soap bubble. The work done in doing so it given by

  1. A \(32 \pi R{ }^{2} T\)
  2. B \(24 \pi R^{2} T\)
  3. C \(8 \pi R^{2} T\)
  4. D \(4 \pi R^{2} T\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(32 \pi R{ }^{2} T\)

Step-by-step Solution

Detailed explanation

Surface energy of a bubble
\(
\begin{array}{l}
E=\text { Tension } \times \text { surface area } \\
E=T \times A
\end{array}
\)
For soap bubble
\(
\begin{array}{l}
E=2 T \times A \\
E=2 T \times 4 \pi R^{2}
\end{array}
\)
Here, \(\quad R=\) radius of bubble
If radius is doubled then we have
\(
\begin{array}{l}
E^{\prime}=2 T \times 4 \pi R^{2} \\
E^{\prime}=2 T \times 4 \pi(2 R)^{2} \\
E^{\prime}=32 \pi R^{2} T
\end{array}
\)