JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Fluid Mechanics

A spherical liquid drop of radius R acquires the terminal velocity

v_{1}

when falls through a gas of viscosity

η

. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity

v_{2}

falling through the same gas. The ratio of terminal velocities

v_{1} / v_{2}

is ____.

(A)4
(B)0.25
(C)32
(D)16✓ Correct

Answer: (D)

Solution

Conserving volume when the drop of radius

R

splits into

64

equal droplets,

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

, so

r = \frac{R}{4}

. By Stokes' law the terminal velocity varies as the square of the radius,

v \propto R^{2}

. Therefore

\frac{v _{1}}{v _{2}} = (\frac{R}{r})^{2} = 4^{2} = 16

. The ratio of terminal velocities is

16

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Single correct option

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