MHT CET · Physics · Mechanical Properties of Fluids
The excess pressure inside a spherical drop of water is three times that of another
drop of water. The ratio of their surface area is
- A \(3: 1\)
- B \(6: 1\)
- C \(1: 9\)
- D \(1: 3\)
Answer & Solution
Correct Answer
(C) \(1: 9\)
Step-by-step Solution
Detailed explanation
Excess pressure \(p=\frac{2 T}{r}\)
\(\frac{p_{1}}{p_{2}}=\frac{r_{2}}{r_{1}}=3\)
\(\begin{array}{l}
\therefore r_{2}=3 r_{1} \\
\frac{A_{1}}{A_{2}}=\frac{\pi r_{1}^{2}}{\pi r_{2}^{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{2}=\frac{1}{(3)^{2}}=\frac{1}{9}
\end{array}\)
\(\frac{p_{1}}{p_{2}}=\frac{r_{2}}{r_{1}}=3\)
\(\begin{array}{l}
\therefore r_{2}=3 r_{1} \\
\frac{A_{1}}{A_{2}}=\frac{\pi r_{1}^{2}}{\pi r_{2}^{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{2}=\frac{1}{(3)^{2}}=\frac{1}{9}
\end{array}\)
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