MHT CET · Physics · Mechanical Properties of Fluids
A frame made of metallic wire enclosing a surface area \(A\) is covered with a soap film. If the area of the frame of metallic wire is reduced by \(50 \%\), the energy of the soap film will be changed by
- A \(100 \%\)
- B \(75 \%\)
- C \(50 \%\)
- D \(25 \%\)
Answer & Solution
Correct Answer
(C) \(50 \%\)
Step-by-step Solution
Detailed explanation
Surface energy \(=\) surface tension \(\times\) surface area
\(
E=T \times 2 A
\)
New surface energy,
\(
E_{1}=T \times 2\left(\frac{A}{2}\right)=T \times A
\)
\(\%\) decrease in surface energy
\(
\begin{array}{l}
=\frac{E-E_{1}}{E} \times 100 \\
=\frac{2 T A-T A}{2 T A} \times 100=50 \%
\end{array}
\)
\(
E=T \times 2 A
\)
New surface energy,
\(
E_{1}=T \times 2\left(\frac{A}{2}\right)=T \times A
\)
\(\%\) decrease in surface energy
\(
\begin{array}{l}
=\frac{E-E_{1}}{E} \times 100 \\
=\frac{2 T A-T A}{2 T A} \times 100=50 \%
\end{array}
\)
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