Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: The ideal fluid do not have shear stress. Reason R: The Newtonian fluid is the fluid in which shear stress is not proportional to rate of shear strain. In the light of the above statements, choose the most appropriate answer from the options given below

• A. Both A and R are correct and R is the correct explanation of A
• B. Both A and R are correct but R is NOT the correct explanation of A
• C. A is correct but R is not correct
• D. A is not correct but R is correct

Hint:

For Newtonian fluid: \[ \boxed{ \tau = \mu \frac{du}{dy} } \] For ideal fluid: \[ \boxed{ \mu = 0 \Rightarrow \tau = 0 } \]

Answer 1

The Correct Option is C

Concept: An ideal fluid is a hypothetical fluid having:
• Zero viscosity
• No shear resistance
• No energy loss due to friction Newtonian fluid follows Newton’s law of viscosity where: \[ \tau \propto \frac{du}{dy} \] that means shear stress is directly proportional to rate of shear strain.

Step 1: Analyzing Assertion A. Assertion A states: \[ \text{“The ideal fluid do not have shear stress.”} \] This statement is correct. Reason:
• Ideal fluid has zero viscosity
• Shear stress exists because of viscosity
• With zero viscosity, shear stress becomes zero Mathematically: \[ \tau = \mu \frac{du}{dy} \] For ideal fluid: \[ \mu = 0 \] Therefore: \[ \tau = 0 \] Hence: \[ \boxed{ \text{Assertion A is correct} } \]

Step 2: Analyzing Reason R. Reason R states: \[ \text{“The Newtonian fluid is the fluid in which shear stress is not proportional to rate of shear strain.”} \] This statement is incorrect. Actually for Newtonian fluid: \[ \tau \propto \frac{du}{dy} \] or \[ \tau = \mu \frac{du}{dy} \] Thus:
• Shear stress is directly proportional to velocity gradient
• Newtonian fluid obeys Newton’s law of viscosity Hence: \[ \boxed{ \text{Reason R is incorrect} } \]

Step 3: Selecting the correct option. We conclude:
• Assertion A is true
• Reason R is false Therefore: \[ \boxed{ (C) } \] is the correct answer. Final Conclusion: Ideal fluids have zero shear stress because viscosity is zero, whereas Newtonian fluids obey proportionality between shear stress and velocity gradient. Hence the correct answer is: \[ \boxed{ (C) } \]