A rain drop of radius 'r' fall in air with a terminal speed vt what is the terminal speed of radius 2r
Correct answer: C. 4Vt
- A. Vt√2
- B. Vt
- C. 4Vt
- D. 2Vt
Explanation
The terminal velocity of a raindrop is governed by the balance between gravitational force and drag force. For a spherical raindrop moving through air, the drag force is proportional to the square of its radius. When the radius is doubled, the terminal velocity is proportional to the square of the new radius, leading to an increase by a factor of 4 (since (2r)^2 = 4r^2). Therefore, the terminal speed becomes 4Vt. Option A incorrectly assumes a simple square root relationship, Option B ignores the change in radius, and Option D assumes a linear increase, all of which are incorrect.
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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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