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Eight equal drops of water are falling through air with a steady speed of 10 cm s⁻¹. If the drops coalesce, the new steady speed is

Asked in JEE Main 11th April 2nd Shift 2023 · Coalescing and splitting drops

• (1) 16 cm s⁻¹
• (2) 40 cm s⁻¹
• (3) 10 cm s⁻¹
• (4) 5 cm s⁻¹

Step-by-step solution

Why the other options are wrong

• (1) comes from no consistent slip lands here; the live routes are R=2r with v∝ r² (the key, 40), v∝ r (20) and v∝ r³ (80), so 16 is a filler.
• (3) comes from assumes the merged drop keeps falling at the same speed, which would need the terminal velocity to be independent of size; v∝ r² says otherwise.
• (4) comes from halves the speed, from treating a bigger drop as something the air slows down more; the weight grows as r³ while the drag only grows as r, so a larger drop always falls faster.

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