Two raindrops reach the earth with their terminal velocities in the ratio 4 : 9 . The ratio of their radii is

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Two raindrops reach the earth with their terminal velocities in the ratio

4 : 9

. The ratio of their radii is

PhysicsMechanical Properties of FluidsNEET

Options:

A $4 : 9$
B $2 : 3$
C $3 : 2$
D $9 : 4$

Solution:

1189 Upvotes Verified Answer

The correct answer is:

2 : 3

Terminal speed is

v = \frac{2 r_{}^{2} g}{9 η} (σ - ρ)

therefore

v \propto r^{2}

\frac{r_{1}}{r_{2}} = \sqrt{\frac{v_{1}}{v_{2}}}

\frac{r_{1}}{r_{2}} = \sqrt{\frac{4}{9}}

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

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