The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is $20 \mathrm{~cm} / \mathrm{s}$. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be \_\_\_\_ $\mathrm{cm} / \mathrm{s}$.

JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Fluid Mechanics

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

Answer: 5

Solution

Terminal velocity is proportional to the square of the radius:

v_{T} \propto r^{2}

. Therefore,

\frac{( v _{T} ) _{1}}{( v _{T} ) _{2}} = (\frac{r _{1}}{r _{2}})^{2} = (\frac{6}{3})^{2} = 4

. Given

(v_{T})_{1} = 20

cm/s, we get

(v_{T})_{2} = \frac{20}{4} = 5

cm/s.

JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Integer answer

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 →
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 →
A cubical block of density ρ_b = 600 kg/m³ floats in a liquid of density ρ_e = 900 kg/m³. If the height of block is H = 8.0 cm then height of the submerged part is ____ cm.
JEE Main 2026View solution →