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BITSAT 2010
Exam
BITSAT
Year
2010
Subject
Physics
Chapter
Mechanical Properties of Fluids

BITSAT 2010 · Physics · Mechanical Properties of Fluids

Two mercury drops (each of radius r ) merge to form a bigger drop....

Two mercury drops (each of radius r\mathrm{r} ) merge to form a bigger drop. The surface energy of the bigger drop, if T\mathrm{T} is the surface tension, is

Options

  1. A25/3πr2T2^{5 / 3} \pi r^{2} T
  2. B4π\mathrmr2T4 \pi \mathrmr^{2} \mathrm{ T}
  3. C2π2T2 \pi^{2} T
  4. D28/3π\mathrmr2T2^{8 / 3} \pi \mathrmr^{2} \mathrm{ T}

Correct answer

D. 28/3π\mathrmr2T2^{8 / 3} \pi \mathrmr^{2} \mathrm{ T}

Step-by-step solution

43πR3=2×43πr3⇒R=21/3r\frac{4}{3} \pi R^{3}=2 \times \frac{4}{3} \pi r^{3} \Rightarrow \mathrm{R}=2^{1 / 3} \mathrm{r} Surface energy of bigger drop, E=4πR2T=4×22/3πr2T=28/3πr2T\mathrm{E}=4 \pi R^{2} T=4 \times 2^{2 / 3} \pi r^{2} T=2^{8 / 3} \pi r^{2} T
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