The terminal velocity ( $\mathrm{v}_{\mathrm{t}}$ ) of the spherical rain drop depends on the radius ( $r$ ) of the spherical rain drop as:-

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Fluid Mechanics

The terminal velocity (

v_{t}

) of the spherical rain drop depends on the radius (

r

) of the spherical rain drop as:-

(A) $r^{1/2}$
(B)r
(C) $r^{2}$ ✓ Correct
(D) $r^{3}$

Answer: (C)

Solution

Terminal velocity of a spherical object falling through a viscous medium is given by Stokes' law:

v_{t} = \frac{2}{9} \frac{g r ^{2} ( ρ _{p} - ρ _{l} )}{η}

where

r

is the radius,

ρ_{p}

is the density of the particle,

ρ_{l}

is the density of the liquid, and

η

is the viscosity.

Clearly,

v_{t} \propto r^{2}

.

Answer: (C)

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Fluid Mechanics →

More JEE Main questions on Fluid Mechanics

Given below are two statements:
Statement I: Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to inter …
JEE Main 2026View solution →
When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by $1%$ each, then the height of the liquid in the tube …
JEE Main 2026View solution →
Surface tension of two liquids (having same densities), $T_{1}$ and $T_{2}$ , are measured using capillary rise method utilizing two tubes with inner radii of $r_{1}$ and $r_{2}$ where $r_{1} > r_{2}$ . The measured liquid heights in these tubes are …
JEE Main 2026View solution →
The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is $20 cm / s$ . The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be
____ $cm / s$ .
JEE Main 2026View solution →
A small metallic sphere of diameter 2 mm and density $10.5$ g/cm³ is dropped in glycerine having viscosity 10 Poise and density $1.5$ g/cm³ respectively. The terminal velocity attained by the sphere is $____$ cm/s.
( $π = \frac{22}{7}$ and $g = 10$ m/s²)
JEE Main 2026View solution →
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 ______ $cm / s$ .
JEE Main 2026View solution →