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 combine, then the excess pressure inside the bigger drop is
- A \(2\) units
- B \(1\) unit
- C \(3\) units
- D \(4\) units
Answer & Solution
Correct Answer
(C) \(3\) units
Step-by-step Solution
Detailed explanation
Given \(P_{\text {in }}-P_{\text {out }}=\frac{4 T}{r}=9\) units If 27 such drop coalesee \(27\left(\frac{4}{3} \pi r^{3}\right)=\frac{4}{3} \pi r_{b}^{3}\)
\(\therefore \quad 3 r=r_{b}\)
\(\therefore\) Excess pressure \(\frac{4 \mathrm{~T}}{\mathrm{r}_{\mathrm{b}}}=\frac{4 \mathrm{~T}}{3 \mathrm{r}}=\frac{9}{3}=3\) unit
\(\therefore \quad 3 r=r_{b}\)
\(\therefore\) Excess pressure \(\frac{4 \mathrm{~T}}{\mathrm{r}_{\mathrm{b}}}=\frac{4 \mathrm{~T}}{3 \mathrm{r}}=\frac{9}{3}=3\) unit
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