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 .

Physics · Mechanical Properties of Matter

JEE Main 2026 — 24 January, Morning Shift — Question 47

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

Answer: 160

Numerical answer — enter this value.

Step-by-step solution

$\mathrm{V}_{\mathrm{T}}=\frac{2 \mathrm{r}^{2} \mathrm{~g}}{9 \mathrm{n}}[\sigma-\rho]$ $\mathrm{V}_{\mathrm{T}} \propto \mathrm{r}^{2}$ $64\left(\frac{4}{3} \pi R_{1}^{3}\right)=\frac{4}{3} \pi R_{2}^{3}$ $\mathrm{R}_{2}=4 \mathrm{R}_{1}$ $\frac{\left(\mathrm{V}_{\mathrm{T}}\right)_{1}}{\left(\mathrm{~V}_{\mathrm{T}}\right)_{2}}=\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{2}=\left(\frac{1}{4}\right)^{2}$ $\frac{10}{\left(\mathrm{~V}_{\mathrm{T}}\right)_{2}}=\frac{1}{16}$ $\left(\mathrm{V}_{\mathrm{T}}\right)_{2}=160 \mathrm{~cm} / \mathrm{sec}$

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Exam: JEE Main 2026
Paper: 24 January, Morning Shift
Subject: Physics
Chapter: Mechanical Properties of Matter
Topic: Viscosity