Q135 / 160 · AP EAMCET 2008 · Physics

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

  • A
    $3: 2$
  • B
    $4:9$
  • C
    $9:4$
  • Correct answer
    D
    $27:8$

Solution

Terminal velocity, $v_T \propto r^2$ $$ \begin{aligned} & \frac{v_{T_1}}{v_{T_2}}=\frac{r_1^2}{r_2^2} \\ & \sqrt{\frac{9}{4}}=\frac{r_1}{r_2} \\ & \frac{r_1}{r_2}=\frac{3}{2} \\ & v=\frac{4}{3} \pi r^3 \\ & \frac{v_1}{v_2}=\frac{r_1^3}{r_2^3}=\frac{27}{8} \\ & \end{aligned} $$

Hence, the correct answer is option: 'D'.

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