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

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

EAMCETEAMCET 2008

Solution:

Terminal velocity, $v_{T} \propto r^{2}$
or $\frac{v_{T_{1}}}{v_{T_{2}}}=\frac{r_{1}^{2}}{r_{2}^{2}}$
$\therefore \sqrt{\frac{9}{4}}=\frac{r_{1}}{r_{2}}$
or $\frac{r_{1}}{r_{2}}=\frac{3}{2}$
$\therefore v=\frac{4}{3} \pi r^{3}$
or $\frac{v_{1}}{v_{2}}=\frac{r_{1}^{3}}{r_{2}^{3}}$
$=\frac{27}{8}$