JEE Main · 2026 · 23 Jan 2026 · Shift 2 · Fluid Mechanics

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)

(A)2.0✓ Correct
(B)1.0
(C)3.0
(D)1.5

Answer: (A)

Solution

The terminal velocity of a sphere settling in a viscous liquid is

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

. In CGS units

r = 0.1 cm

ρ_{b} - ρ_{ℓ} = 10.5 - 1.5 = 9 g/cm^{3}

g = 1000 cm/s^{2}

and

η = 10 poise

. Substituting,

v_{T} = \frac{2 ( 0.1 ) ^{2} ( 9 ) ( 1000 )}{9 \times 10} = \frac{2 \times 0.01 \times 9 \times 1000}{90} = 2.0 cm/s

. The terminal velocity is

2.0 cm/s

JEE Main · 2026 · 23 Jan 2026 · Shift 2 · Single correct option

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