Eight equal drops of water are falling through air with a steady speed of 10 cm/s. If the drops coalesce, the new velocity is??[2023]

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Solution

Q.
Eight equal drops of water are falling through air with a steady speed of 10 cm/s. If the drops coalesce, the new velocity is [2023]

1 10 cm/s

2 40 cm/s

3 16 cm/s

4 5 cm/s

Ans.
(2)

$v \propto r^{2}$

$\Rightarrow \frac{v_{1}}{v_{2}} = {(\frac{r}{R})}^{2}$

$8 \cdot \frac{4}{3} π r^{3} = \frac{4}{3} π R^{3}$

$R = 2 r$

$\Rightarrow \frac{10}{v_{2}} = {(\frac{1}{2})}^{2} \Rightarrow v_{2} = 40 cm/s$

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