MHT CET · Physics · Mechanical Properties of Fluids

What should be the diameter of a soap bubble, in order that the excess pressure inside it is \(25.6 \mathrm{Nm}^{-2}\) ? [surface tension of soap solution \(\left.=3.2 \times 10^{-2} \mathrm{Nm}^{-2}\right]\)

A \(2 \mathrm{~cm}\)
B \(1.5 \mathrm{~cm}\)
C \(1 \mathrm{~cm}\)
D \(0.5 \mathrm{~cm}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1 \mathrm{~cm}\)

Step-by-step Solution

Detailed explanation

The formula for excess pressure inside the bubble is given as \(P_0=\frac{4 T}{R}\)
Where, \(\mathrm{T}\) is surface tension and \(\mathrm{R}\) is the radius of the sphere
Rearranging the formula for \(\mathrm{R}\) and substituting the values,
\(\begin{aligned}
& R=\frac{4 T}{P_0} \\
& R=\frac{4 \times 3.2 \times 10^{-2}}{25.6} \\
& R=0.5 \times 10^{-2} \mathrm{~m}=0.5 \mathrm{~cm}
\end{aligned}\)
The diameter then becomes, \(2 \mathrm{R}=1 \mathrm{~cm}\)

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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