"n" equal rain drops each of radius 2mm fall with terminal velocity of 8cms-1 each, if coalesce then Vt=32cms-1, what about n=?
Correct answer: A. 8
- A. 8
- B. 4
- C. 2
- D. 16
Explanation
The terminal velocity of a droplet is given by the relation Vt ∝ r2. When n droplets of radius 2mm coalesce into a single droplet, the volume of the new droplet is n times that of one droplet, hence its radius becomes r' = 2mm * n1/3. The new terminal velocity Vt is 32cms-1. Since Vt is proportional to the square of the radius, (r')2 = 4n2/3. Solving for n gives n = 8. This matches Option A. The other options do not satisfy the volume and velocity relationship correctly.
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