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JIPMER 2018
Exam
JIPMER
Year
2018
Subject
Physics
Chapter
Mechanical Properties of Fluids

JIPMER 2018 · Physics · Mechanical Properties of Fluids

A rain drop of radius 0.3 mm has a terminal velocity in air 1 ~ms^...

A rain drop of radius 0.3 mm has a terminal velocity in air 1 ms−11 \mathrm{~ms}^{-1}. The viscosity of air is 18×10−518 \times 10^{-5} poise. Find the viscous force on the rain drops.

Options

  1. A2.05×10−7 N2.05 \times 10^{-7} \mathrm{~N}
  2. B1.018×10−7 N1.018 \times 10^{-7} \mathrm{~N}
  3. C1.05×10−7 N1.05 \times 10^{-7} \mathrm{~N}
  4. D2.058×10−7 N2.058 \times 10^{-7} \mathrm{~N}

Correct answer

B. 1.018×10−7 N1.018 \times 10^{-7} \mathrm{~N}

Step-by-step solution

Here, r=0.3 mm=0.3×10−3 m,v=1 ms−1η=18×10−5\mathrm{r}=0.3 \mathrm{~mm}=0.3 \times 10^{-3} \mathrm{~m}, \mathrm{v}=1 \mathrm{~ms}^{-1} \eta=18 \times 10^{-5} poise =18×10−6=18 \times 10^{-6} decapoise Viscous force, F=6πηrv\mathrm{F}=6 \pi \eta \mathrm{rv}=6×227×(18×10−6)×(0.3×10−3)×1=1.018×10−7 N\begin{aligned} & =6 \times \frac{22}{7} \times\left(18 \times 10^{-6}\right) \times\left(0.3 \times 10^{-3}\right) \times 1 \\ & =1.018 \times 10^{-7} \mathrm{~N}\end{aligned}$$
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