If an air bubble of diameter 2 mm rises steadily through a liquid of density $2000 \mathrm{~kg} / \mathrm{m}^{3}$ at a rate of $0.5 \mathrm{~cm} / \mathrm{s}$, then the coefficient of viscosity of liquid is $\_\_\_\_$ Poise. (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$)

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Fluid Mechanics

If an air bubble of diameter 2 mm rises steadily through a liquid of density

2000 kg / m^{3}

at a rate of

0.5 cm / s

, then the coefficient of viscosity of liquid is

____

Poise. (Take

g = 10 m / s^{2}

)

Answer: (B)

Rising at a steady (terminal) velocity, the net buoyant force on the bubble balances the viscous drag,

\frac{4}{3} π R^{3} ρ_{ℓ} g = 6 π η R v

(the air bubble's own weight being negligible). Hence

η = \frac{2}{9} \frac{ρ _{ℓ} R ^{2} g}{v}

. With

R = 1 0^{- 3} m

ρ_{ℓ} = 2000 kg/m^{3}

g = 10 m/s^{2}

and

v = 5 \times 1 0^{- 3} m/s

η = \frac{2}{9} \times \frac{2000 \times ( 1 0 ^{- 3} ) ^{2} \times 10}{5 \times 1 0 ^{- 3}} = \frac{8}{9} Pa \cdot s = 0.889 Pa \cdot s

. Since

1 Pa \cdot s = 10

Poise, the coefficient of viscosity of the liquid is

8.8

Poise.

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Single correct option