Two rain drops reach the earth with different terminal velocities having ratio 9:4. Then the ratio of their volumes is
Correct answer: D. 27:8
- A. 3:2
- B. 4:9
- C. 9:4
- D. 27:8
Explanation
The terminal velocity of a spherical object falling through a fluid is proportional to the square root of its volume. Given the ratio of terminal velocities is 9:4, we can deduce the ratio of the volumes by cubing this ratio. Hence, (9/4)^3 = 729/64, which simplifies to 27:8. Therefore, the correct answer is 27:8. Other options fail to account for this cubic relationship between terminal velocity and volume.
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About Fluid Dynamics
Fluid flow is described through speed, pressure and density, including steady flow and the equation of continuity for conserving mass. Bernoulli's equation relates pressure, speed and height, while fluid drag and terminal velocity explain why a falling object eventually moves at constant speed when drag balances its weight.
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