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 .

Physics · Mechanical Properties of Matter

JEE Main 2024 — 8 April, Shift 2 — Question 49

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 $\qquad$ $\mathrm{cm} / \mathrm{s}$ .

Answer: 40

Numerical answer — enter this value.

Step-by-step solution

$\mathrm{m}=$ mass of small drop

$M=$ mass of bigger drop

$\mathrm{V}_{\mathrm{t}}=\frac{2}{9} \frac{\mathrm{R}^{2}(\rho-\sigma) g}{\eta}$

$8 \propto \mathrm{~m}=\mathrm{M}$

$8 \mathrm{r}^{3}=\mathrm{R}^{3} \Rightarrow \mathrm{R}=2 \mathrm{R}$

as $\mathrm{V}_{\mathrm{t}} \times \mathrm{R}^{2} \quad \because$ Radius double so $\mathrm{V}_{\mathrm{t}}$

becomes 4 time

$\therefore 4 \times 10=40 \mathrm{~cm} / \mathrm{s}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 8 April, Shift 2
Subject: Physics
Chapter: Mechanical Properties of Matter
Topic: Viscosity