Question

Match List - I with List - II. 

Choose the correct answer from the options given below : 
 

• A. A-I, B-II, C-III, D-IV
• B. A-III, B-I, C-II, D-IV
• C. A-IV, B-III, C-I, D-II
• D. A-III, B-I, C-IV, D-II

Hint:

Poisson's Ratio is unique because it is dimensionless (a ratio of two strains), unlike the Moduli which all have units of Pressure (Pascals or $N/m^2$).

Answer 1

The Correct Option is D

Step 1: Concept:
The question asks to match fundamental mechanical material properties (elastic moduli) with their mathematical definitions, which are all variations of the formula: $\text{Modulus} = \frac{\text{Stress}}{\text{Strain}}$.

Step 2: Key Formula or Approach:
- Stress is Force per unit area ($F/A$).
- Strain is the fractional deformation (e.g., $\Delta L / L$).

Step 3: Step-by-step Explanation:

• A. Young's Modulus ($Y$ or $E$): Defined as longitudinal stress over longitudinal strain.
$Y = \frac{F/A}{\Delta L/L} = \frac{FL}{A\Delta L}$.
Matches III.

• B. Bulk Modulus ($K$ or $B$): Defined as volumetric stress (Pressure, $dP$) over volumetric strain ($dV/V$). The negative sign ensures the modulus is positive since volume decreases when pressure increases.
$K = -\frac{dP}{dV/V} = -V\frac{dP}{dV}$.
Matches I.

• C. Modulus of Rigidity (Shear Modulus, $G$): Defined as shear stress over shear strain. Shear strain is the lateral displacement ($x$) divided by the height ($h$).
$G = \frac{F/A}{x/h}$.
Matches IV.

• D. Poisson's Ratio ($\nu$): Not a modulus, but a ratio of strains. It is the negative ratio of transverse (lateral) strain to axial (longitudinal) strain.
$\nu = -\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}} = -\frac{\Delta d / d}{\Delta L / L}$.
Matches II.
The complete matching sequence is A-III, B-I, C-IV, D-II.

Step 4: Final Answer:
This sequence aligns with option (D).