Two rain drops reach the earth with different terminal velocities having ratio $9: 4$. Then the ratio of…
Two rain drops reach the earth with different terminal velocities having ratio $9: 4$. Then the ratio of their volumes is
- $3: 2$
- $4:9$
- $9:4$
- $27:8$
Solution
Terminal velocity, $v_T \propto r^2$
$
\begin{aligned}
& \frac{v_{T_1}}{v_{T_2}}=\frac{r_1^2}{r_2^2} \\
& \sqrt{\frac{9}{4}}=\frac{r_1}{r_2} \\
& \frac{r_1}{r_2}=\frac{3}{2} \\
& v=\frac{4}{3} \pi r^3 \\
& \frac{v_1}{v_2}=\frac{r_1^3}{r_2^3}=\frac{27}{8} \\
&
\end{aligned}
$
Asked in: AP EAMCET 2008
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