Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be _______ cm/s.

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Solution

Q.
Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be _______ cm/s. [2024]

Ans.
(40) $m = mass of small drop,$ $M = mass of bigger drop$

$V_{t} = \frac{2}{9} \frac{r^{2} (ρ - σ) g}{η} \Rightarrow V_{t} \propto r^{2}$

$8 m = M \Rightarrow 8 r^{3} = R^{3} \Rightarrow R = 2 r$

$Radius double so V_{t} becomes 4 times :$

$\Rightarrow V_{t} = 4 \times 10 = 40 cm / s$

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