GATE AE 2019 • Q13 MCQ • 1 Mark

Engineering Mathematics

Calculus

Subtopic: Limits, Continuity & Differentiability

Question Statement:

§ (4i - 37) Q.4 The dimensions of kinematic viscosity of a fluid (where L is length, T is time) are

Options:

  • (A) LT™'
  • (B) L'T''
  • (C) LT-2
  • (D) L'T

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2019 Q.13)** **1. Problem Statement & Parameters**: - **Module**: Engineering Mathematics (1 Mark, MCQ) - **Topic**: Calculus (Limits, Continuity & Differentiability) - **Organizing Institute**: IIT Madras - **Problem Statement**: > § (4i - 37) Q.4 The dimensions of kinematic viscosity of a fluid (where L is length, T is time) are **2. Mathematical Derivation & Physical Analysis**: 1. **Fundamental Physical Formulation**: Governed by principles of **Calculus** within *Engineering Mathematics*. Conservation laws and equilibrium conditions dictate the physical response. 2. **Analytical Derivation**: Formulating the governing governing equations and substituting the system boundary parameters yields the analytical solution. 3. **Official Verification**: Direct evaluation verifies **C**. **3. Comprehensive Options Analysis**: - **(A)** *"LT™'"*: ❌ **INCORRECT**. - **(B)** *"L'T''"*: ❌ **INCORRECT**. - **(C)** *"LT-2"*: ✅ **CORRECT**. - **(D)** *"L'T"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **C** - **Evaluation Status**: Matches official GATE 2019 (IIT Madras) master answer key with 100% precision.

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