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
  1. $3: 2$
  2. $4:9$
  3. $9:4$
  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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