Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of $10 \mathrm{~cm} / \mathrm{s}$ coalesce to form a bigger drop. The terminal velocity of bigger drop is ______ $\mathrm{cm} / \mathrm{s}$.

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Fluid Mechanics

Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of

10 cm / s

coalesce to form a bigger drop. The terminal velocity of bigger drop is ______

cm / s

Answer: 160

Solution

The terminal velocity of a falling drop varies as the square of its radius,

v_{T} \propto r^{2}

. Conserving volume when

64

equal drops merge,

64 (\frac{4}{3} π r^{3}) = \frac{4}{3} π R^{3}

, so

R = 4 r

. Hence

\frac{v _{T}^{'}}{v _{T}} = (\frac{R}{r})^{2} = 16

, and

v_{T}^{'} = 16 \times 10 = 160

. The terminal velocity of the larger drop is

160 cm/s

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Integer answer

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