According to the Newton's law of viscosity, the shear stress of a fluid element layer is directly proportional to the:
- Abulk modulus
- Belastic modulus
- Crate of shear strainCorrect
- Dpressure
Solution
Concept
Shear stress in a fluid is directly proportional to the rate of shear strain (velocity gradient).
Formula
τ = μ (du/dy)
Step-by-step solution
1. Newton's law of viscosity: τ = μ (du/dy). 2. du/dy is the velocity gradient, which equals the rate of shear strain (rate of angular deformation). 3. So τ is directly proportional to the rate of shear strain, and μ (dynamic viscosity) is the constant of proportionality. 4. Answer is (C).
Explanation
Newton's law says shear stress in a fluid layer depends on how fast the fluid deforms, not on how much it deforms. The velocity gradient du/dy is the rate of shear strain. Dynamic viscosity μ is the constant that links them.
Why the other options are wrong
A: Bulk modulus relates pressure change to volume change (compressibility), not shear. B: Elastic modulus relates stress to strain in solids, not to the rate of strain. D: Pressure is a normal stress, not shear stress.
Shortcut
Fluid means rate of strain. Solid means strain itself.
Common mistake
Choosing shear strain instead of rate of shear strain. Fluids resist the rate of deformation, not the deformation itself.
Correct answer: C) rate of shear strain