MHT CET · Physics · Mechanical Properties of Fluids

The work done in blowing a soap bubble of radius 'R' is ' \(\mathrm{W}\) '. The work done in blowing a bubble of radius ' \(2 \mathrm{R}^{\prime}\) of the same soap solution is

A \(\frac{\mathrm{w}}{4}\)
B \(\frac{\mathrm{w}}{2}\)
C 4w
D 2w

Verified Solution

Answer & Solution

Correct Answer

(C) 4w

Step-by-step Solution

Detailed explanation

(B)
\(\mathrm{W}_{1}=8 \pi \mathrm{R}^{2} \mathrm{~T}\) where \(\mathrm{T}\) is surface tension.
If radius is doubled and surface tension remains same then \(\mathrm{W}_{2}=8 \pi(2 \mathrm{R})^{2} \mathrm{~T}=8 \pi \mathrm{R}^{2} \mathrm{~T}=4 \mathrm{~W}_{1}\)
However, the solution is heated, the value of surface tension decreases. Hence, \(\mathrm{W}_{2} < 4 \mathrm{~W}_{1}\)

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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