Question

Match List I with List II: 

List I	List II
A. Young’s Modulus	II. $FL / [A(\Delta L)]$
B. Compressibility	I. $(\Delta d / d) / (\Delta L / L)$
C. Bulk Modulus	III. $- (1 / \Delta P)(\Delta V / V)$
D. Poisson’s Ratio	IV. $- V \Delta P / \Delta V$

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

Hint:

Remember that "Modulus" is always a measure of "Stiffness," while "Compressibility" is a measure of how "Squishy" a material is. They are inverses of each other!

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Elastic moduli describe how a material deforms under different types of stress. Each modulus is defined as a specific ratio of stress to strain.

Step 2: Detailed Explanation:

• A $\rightarrow$ II: Young's Modulus ($Y$) is longitudinal stress over longitudinal strain: $Y = \frac{F/A}{\Delta L/L} = \frac{FL}{A\Delta L}$.
• B $\rightarrow$ III: Compressibility ($K$) is the reciprocal of the Bulk Modulus: $K = \frac{1}{B} = -\frac{1}{\Delta P} \frac{\Delta V}{V}$.
• C $\rightarrow$ IV: Bulk Modulus ($B$) is hydraulic stress over volumetric strain: $B = \frac{-\Delta P}{\Delta V / V} = -V \frac{\Delta P}{\Delta V}$.
• D $\rightarrow$ I: Poisson's Ratio ($\sigma$) is the ratio of lateral strain to longitudinal strain: $\sigma = \frac{\Delta d / d}{\Delta L / L}$.

Step 3: Final Answer:
The correct matching is A-II, B-III, C-IV, D-I.