Fluid Mechanics

JEE Main level, single correct, medium

160 of 192

Question 160 of 192

If an air bubble of diameter 22 mm rises steadily through a liquid of density 20002000 kg/m3^3 at a rate of 0.50.5 cm/s, then the coefficient of viscosity of liquid is _______ Poise. (Take g=10g = 10 m/s2^2)

Show answer and solution

Answer: (B) 8.88.8

The terminal velocity of an air bubble rising in a liquid is given by Stokes' law:

v=29r2ρgηv = \dfrac{2}{9} \dfrac{r^2 \rho g}{\eta}

Where:
r=D2=1 mm=10−3 mr = \dfrac{D}{2} = 1 \text{ mm} = 10^{-3} \text{ m}
ρ=2000 kg/m3\rho = 2000 \text{ kg/m}^3
g=10 m/s2g = 10 \text{ m/s}^2
v=0.5 cm/s=5×10−3 m/sv = 0.5 \text{ cm/s} = 5 \times 10^{-3} \text{ m/s}

Rearranging the formula for the coefficient of viscosity η\eta:

η=29r2ρgv\eta = \dfrac{2}{9} \dfrac{r^2 \rho g}{v}

Substituting the given values:

η=29×(10−3)2×2000×105×10−3\eta = \dfrac{2}{9} \times \dfrac{(10^{-3})^2 \times 2000 \times 10}{5 \times 10^{-3}}

η=29×10−6×200005×10−3\eta = \dfrac{2}{9} \times \dfrac{10^{-6} \times 20000}{5 \times 10^{-3}}

η=29×2×10−25×10−3\eta = \dfrac{2}{9} \times \dfrac{2 \times 10^{-2}}{5 \times 10^{-3}}

η=29×4=89 Pa⋅s\eta = \dfrac{2}{9} \times 4 = \dfrac{8}{9} \text{ Pa}\cdot\text{s}

To convert the viscosity from SI units (Pa⋅\cdots) to CGS units (Poise), we multiply by 1010:

η=89×10=809 Poise\eta = \dfrac{8}{9} \times 10 = \dfrac{80}{9} \text{ Poise}

η≈8.88 Poise\eta \approx 8.88 \text{ Poise}

The closest given option is 8.88.8.

Answer: 8.88.8

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Fluid mechanics simulationDrag the sliders and watch the numbers in this question change.

More Physics practice

JEE Main Physics practice question on Fluid Mechanics (Viscosity), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.