JEE Main 2026 Apr 8 Shift 2, Physics Q9: Hydrodynamic

JEE Main2026Apr 8, Shift 2Physics

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
$16$

Solution

Radius of the smaller droplets from volume conservation:

$\frac{4}{3} π R^{3} = 64 \cdot \frac{4}{3} π R_{2}^{3} ⟹ R_{2} = \frac{R}{4}$ .

Terminal velocity (Stokes regime): $v_{T} = \frac{2 ( ρ - σ ) g}{9 η} r^{2} \propto r^{2}$ .

$\frac{v _{1}}{v _{2}} = \frac{R ^{2}}{( R /4 ) ^{2}} = 16$ .

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JEE Main 2026 Apr 8 Shift 2, Physics Q9: Hydrodynamic

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