JEE Main 2026 — Jan 24, Shift 1 — Physics solution

JEE Main2026Jan 24, Shift 1Physics

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.

Your answer

Solution

Find the radius of the combined drop from volume conservation:

$64 \cdot \frac{4}{3} π r^{3} = \frac{4}{3} π R^{3} \Rightarrow R = 4 r$ .

Terminal velocity scaling (Stokes' law): $v_{T} \propto r^{2}$ .

$\frac{V _{T, big}}{V _{T, small}} = (\frac{R}{r})^{2} = 16$ .

$V_{T, big} = 16 \times 10 = 160$ cm/s.

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