MHT CET · Physics · Mechanical Properties of Fluids
One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is
- A 1:1000
- B 1:1
- C \(1: 10\)
- D \(1: 100\)
Answer & Solution
Correct Answer
(C) \(1: 10\)
Step-by-step Solution
Detailed explanation
\(U_{1}=1000 \times 4 \pi r_{1}^{2} \times T\)
\(\frac{r_{2}}{r_{1}}=(1000)^{1 / 3}=10\)
\(U_{2}=4 \pi r_{2}^{2} T\)
\(\frac{U_{2}}{U_{1}}=\frac{4 \pi r_{2}^{2} T}{1000 \times 4 \pi r_{1}^{2} \times T}=\frac{100}{1000}=\frac{1}{10}\)
\(\frac{r_{2}}{r_{1}}=(1000)^{1 / 3}=10\)
\(U_{2}=4 \pi r_{2}^{2} T\)
\(\frac{U_{2}}{U_{1}}=\frac{4 \pi r_{2}^{2} T}{1000 \times 4 \pi r_{1}^{2} \times T}=\frac{100}{1000}=\frac{1}{10}\)
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