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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
NTA AbhyasNTA Abhyas 2022
Solution:
We know that terminal velocity is
given by
$V _{ T }=\frac{2}{9 n } r ^{2}\left(\rho_{ s }-\rho_{1}\right)$
$\therefore \quad V _{ T } \propto r ^{2}$
$\therefore \quad \frac{9}{4}=\left(\frac{ r _{1}}{ r _{2}}\right)^{2}$
$\therefore \quad \frac{r_{1}}{r_{2}}=\frac{3}{2}$
$\therefore \quad \frac{ V _{1}}{ V _{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{3}=\left(\frac{3}{2}\right)^{3}$
$\frac{ V _{1}}{ V _{2}}=27: 8$