COMEDK · Physics · 11. Mechanical Properties of Fluids

While falling through the air, twenty seven droplets having the same radius 1 mm and terminal velocity \(10 \mathrm{cms}^{-1}\) combine to form a single drop. What is the terminal velocity of the single bigger drop?

A \(30 \mathrm{cms}^{-1}\)
B \(20 \mathrm{cms}^{-1}\)
C \(60 \mathrm{cms}^{-1}\)
D \(90 \mathrm{cms}^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(90 \mathrm{cms}^{-1}\)

Step-by-step Solution

Detailed explanation

Let \(r\) be the radius of each small droplet and \(R\) be the radius of the single large drop. Since the volume is conserved, we have \(27 \times \dfrac{4}{3} \pi r^{3} = \dfrac{4}{3} \pi R^{3}\). This implies \(R^{3} = 27 r^{3}\), so \(R = 3r\). The terminal velocity \(v\) of…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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