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

JIPMER 2010 · Physics · Mechanical Properties of Fluids

64 spherical rain drops of equal size are falling vertically...

64 spherical rain drops of equal size are falling vertically through air with a terminal velocity 1.5 ms−11.5 \mathrm{~ms}^{-1}. If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is

Options

  1. A8 ms−18 \mathrm{~ms}^{-1}
  2. B16 ms−116 \mathrm{~ms}^{-1}
  3. C24 ms−124 \mathrm{~ms}^{-1}
  4. D32 ms−132 \mathrm{~ms}^{-1}

Correct answer

C. 24 ms−124 \mathrm{~ms}^{-1}

Step-by-step solution

Volume of big drop =64×=64 \times volume of a small drop ⇒43πR3=64×43πr3⇒R=4r\Rightarrow \frac{4}{3} \pi R^3=64 \times \frac{4}{3} \pi r^3 \Rightarrow R=4 r The terminal velocity of spherical rain drop v=2r2(ρ−σ)9η⇒v∝r2⇒v1v2=(rR)2=(14)2=116∴v2=16v1=16×1.5=24 ms−1\begin{aligned} & v=\frac{2 r^2(\rho-\sigma)}{9 \eta} \Rightarrow v \propto r^2 \\ \Rightarrow \quad & \frac{v_1}{v_2}=\left(\frac{r}{R}\right)^2=\left(\frac{1}{4}\right)^2=\frac{1}{16} \\ \therefore \quad & v_2=16 v_1=16 \times 1.5=24 \mathrm{~ms}^{-1} \end{aligned}
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