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 the bigger drop is ______ cm/s. [2026]

Question

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 the bigger drop is ______ cm/s. [2026]

Smart Achievers · Accepted Answer

(160)

$V_{T} = \frac{2 r^{2} g}{9 η} (σ - ρ)$

$V_{T} \propto r^{2}$

$64 drops$

$64 (\frac{4}{3} π R_{1}^{3}) = \frac{4}{3} π R_{2}^{3}$

$R_{2} = 4 R_{1}$

$\frac{{(V_{T})}_{1}}{{(V_{T})}_{2}} = {(\frac{R_{1}}{R_{2}})}^{2} = {(\frac{1}{4})}^{2}$

$\frac{10}{{(V_{T})}_{2}} = \frac{1}{16}$

${(V_{T})}_{2} = 160 cm/sec$

Solution

Q.
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 the bigger drop is ______ cm/s. [2026]

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Solution

Q. 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 the bigger drop is ______ cm/s. [2026]

Ans. (160) VT=2r2g9η(σ-ρ) VT∝r2 64 drops 64(43πR13)=43πR23 R2=4R1 (VT)1(VT)2=(R1R2)2=(14)2 10(VT)2=116 (VT)2=160 cm/sec

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Q.
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 the bigger drop is ______ cm/s. [2026]