COMEDK · Physics · 11. Mechanical Properties of Fluids
64 rain drops of the same radius are falling through air with a steady velocity of \(0.5 \mathrm{~cm} \mathrm{~s}^{-1}\). If the drops coalesce, the terminal velocity would be
- A \(0.08 \mathrm{~ms}^{-1}\)
- B \(1.25 \mathrm{~ms}^{-1}\)
- C \(0.8 \mathrm{~ms}^{-1}\)
- D \(1.25 \mathrm{~cm} \mathrm{~s}^{-1}\)
Answer & Solution
Correct Answer
(A) \(0.08 \mathrm{~ms}^{-1}\)
Step-by-step Solution
Detailed explanation
Let \(r\) be the radius of each small drop and \(v\) be its terminal velocity. The terminal velocity of a spherical drop is given by Stokes Law as \(v = \dfrac{2}{9} \dfrac{r^2(\rho - \sigma)g}{\eta}\), where \(\rho\) is the density of the drop, \(\sigma\) is the density of air,…
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