A small drop of water falls from rest through a large height 'h' in air, the final velocity is
Correct answer: D. Almost independent of h
- A. α√h
- B. α h
- C. α (1/h)
- D. Almost independent of h
Explanation
As a small drop of water falls through the air, it experiences forces due to gravity and air resistance. Initially, gravity causes the drop to accelerate, but as its speed increases, so does the air resistance acting against it. Eventually, the drop reaches a point where the downward gravitational force is balanced by the upward drag force of air resistance, and it falls at a constant terminal velocity. This terminal velocity is primarily dependent on the size and density of the drop, as well as the density of the air, but it is almost independent of the height from which the drop falls. Therefore, the correct answer is that the final velocity is almost independent of h.Options suggesting a relationship with height (α√h, α h, α (1/h)) are incorrect because they do not account for the terminal velocity condition where height does not play a significant role in determining the final velocity.
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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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