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Q.

1000 equal drops of water are falling through air with a steady speed of 20 cm/sec. If the drops coalesce, then the new velocity is :

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a

1000 cm/s

b

1500 cm/s

c

2000 cm/s

d

3000 cm/s

answer is C.

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Detailed Solution

$v \propto r^{2} \frac{v_{1}}{v_{2}} = {(\frac{r}{R})}^{2}$
Volume conservation
$1000 \times \frac{4}{3} π {(r)}^{3} = \frac{4}{3} π R^{3} 10 r = R \frac{r}{R} = \frac{1}{10} \frac{20}{v} = {(\frac{1}{10})}^{2} \frac{20}{v} = \frac{1}{100} v = 2000 c m / s$

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