TS EAMCET · Physics · Mechanical Properties of Fluids
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 \(9:4\)
- D \(27:8\)
Answer & Solution
Correct Answer
(D) \(27:8\)
Step-by-step Solution
Detailed explanation
Terminal velocity, \(v_T \propto r^2\) \[ \begin{aligned} & \frac{v_{T_1}}{v_{T_2}}=\frac{r_1^2}{r_2^2} \\ & \sqrt{\frac{9}{4}}=\frac{r_1}{r_2} \\ & \frac{r_1}{r_2}=\frac{3}{2} \\ & v=\frac{4}{3} \pi r^3 \\ & \frac{v_1}{v_2}=\frac{r_1^3}{r_2^3}=\frac{27}{8} \\ & \end{aligned} \]
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