COMEDK · Physics · 11. 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 \(50 \%\), then the energy of the soap film will be changed by

A \(100 \%\)
B \(75 \%\)
C \(50 \%\)
D \(25 \%\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(50 \%\)

Step-by-step Solution

Detailed explanation

Given, initial surface area, \(A_{1}=A\) Final surface area, \(A_{2}=A_{1}-50 \%\) of \(A\) \(A_{2}=A-50 \%\) of \(A=A-\frac{A}{2}=\frac{A}{2}\) Initial surface energy, \(E_{1}=T \cdot 2 A=2 T A\) Final surface energy, \(E_{2}=\) Surface tension \(\times\) Surface…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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