MHT CET · Physics · Mechanical Properties of Fluids

Due to surface tension, the excess pressure inside a smaller drop is 9 units. If 27 smaller drops of same liquid combine then the excess pressure inside the bigger drop is

A 18 units
B 9 units
C 6 units
D 3 units

Verified Solution

Answer & Solution

Correct Answer

(D) 3 units

Step-by-step Solution

Detailed explanation

Excess pressure Or Pressure jump \(=2\left(\frac{\sigma}{r}\right)=9\) units
If 27 such drops combine, total volume is: \(\mathrm{V}_{\mathrm{B}}=27 \mathrm{~V}_{\mathrm{S}}\)
Using volume conservation:
\(\begin{aligned}
& \frac{4}{3} \pi \mathrm{R}^3=27\left(\frac{4}{3} \pi \mathrm{R}^3\right) \\
& \Rightarrow \mathrm{R}=(3 \mathrm{r}) \\
& \therefore \text { Excess pressure }=\frac{2 \sigma}{\mathrm{R}}=\frac{2 \sigma}{3 \mathrm{r}}=3 \text { units }
\end{aligned}\)

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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