Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of $10 \mathrm{~cm} / \mathrm{s}$. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be ______ $\mathrm{cm} / \mathrm{s}$.

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Fluid Mechanics

Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of

10 cm / s

. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be ______

cm / s

Answer: 40

Solution

Terminal velocity

V_{t} \propto r^{2}

(Stokes' law).
Volume is conserved on coalescence:

8 (\frac{4}{3} π r^{3}) = \frac{4}{3} π R^{3} ⟹ R^{3} = 8 r^{3} ⟹ R = 2 r

V_{t}^{'} = V_{t} (\frac{R}{r})^{2} = 10 \times 4 = 40 cm/s

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Integer answer

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