The shear stress at a point in a liquid is found to be 0.02 N/m². The velocity gradient at this point is 0.20 s⁻¹. What will be the viscosity of the liquid (in Poise)?
- A0.4
- B10
- C1Correct
- D2
Solution
Concept
Newton's law of viscosity: shear stress = dynamic viscosity × velocity gradient.
Formula
τ = μ (du/dy), so μ = τ / (du/dy); 1 N·s/m² = 10 Poise
Step-by-step solution
1. Given τ = 0.02 N/m² and du/dy = 0.20 s⁻¹. 2. μ = τ / (du/dy) = 0.02 / 0.20 = 0.1 N·s/m². 3. Convert to Poise: 1 N·s/m² = 10 Poise. 4. μ = 0.1 × 10 = 1 Poise.
Explanation
Viscosity is shear stress divided by velocity gradient. This gives 0.1 N·s/m² in SI units. Since 1 N·s/m² equals 10 Poise, the answer is 1 Poise.
Why the other options are wrong
A (0.4): wrong unit conversion or arithmetic. B (10): uses 1 N·s/m² = 100 Poise, or forgets that the SI value is 0.1. D (2): arithmetic error.
Shortcut
μ (Poise) = 10 × τ/(du/dy) when τ is in N/m² = 10 × 0.1 = 1.
Common mistake
Leaving the answer as 0.1 in SI units, or using the wrong factor (1 N·s/m² = 10 Poise, not 100).
Correct answer: C) 1