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MHT CET · Physics · Mechanical Properties of Fluids

Let ' \(W_1\) ' be the work done in blowing a soap bubble of radius ' \(r\) ' from soap solution at room temperature. The soap solution is now heated and second soap bubble of radius ' \(2 \mathrm{r}\) ' is blown from the heated soap solution. If ' \(\mathrm{W}_2\) ' is the work done in forming this bubble then

  1. A \(\mathrm{W}_2=2 \mathrm{~W}_1\)
  2. B \(\mathrm{W}_2=4 \mathrm{~W}_1\)
  3. C \(\mathrm{W}_2>4 \mathrm{~W}_1\)
  4. D \(\mathrm{W}_2 < 4 \mathrm{~W}_1\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\mathrm{W}_2 < 4 \mathrm{~W}_1\)

Step-by-step Solution

Detailed explanation

\(
\mathrm{W}_1=8 \pi \mathrm{r}^2 \mathrm{~T}
\)
Where, \(\mathrm{T}=\) surface tension
\(
\mathrm{W}_2=8 \pi(2 \mathrm{r})^2 \mathrm{~T}^{\prime}=32 \pi \mathrm{r}^2 \mathrm{~T}^{\prime}
\)
Since soap solution is heated, its surface tension decrease.
\(
\begin{aligned}
& \therefore \mathrm{T}^{\prime} < \mathrm{T} \\
& \therefore \mathrm{W}_2 < 4 \mathrm{~W}_1
\end{aligned}
\)