Two rain drops reach the earth with different terminal velocities having ratio 9:4. Then the ratio of their volume is

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Two rain drops reach the earth with different terminal velocities having ratio 9:4. Then the ratio of their volume is

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3:2

27:8

4:9

9:4

answer is D.

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Detailed Solution

$V_{t} = \frac{2}{9} \frac{{gr}^{2} [ρ - σ]}{n} \Rightarrow V_{t} \propto r^{2} \propto {(V^{1 / 3})}^{2} \propto V^{2 / 3}$

$\frac{v_{t_{1}}}{v_{t_{2}}} = {(\frac{r_{1}}{r_{2}})}^{2}$

$\frac{9}{4} = {(\frac{r_{1}}{r_{2}})}^{2}$

$\frac{r_{1}}{r_{2}} = \frac{3}{2}$

$their volumes are in the ratio = {(\frac{r_{1}}{r_{2}})}^{3} = \frac{27}{8}$

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