Match List I with List II :List I List II A. Young's Modulus I. $\frac{\Delta d}{\Delta L} ( \frac{L}{d})$ B. Compressibility II. $\frac{FL}{A(\Delta L)}$ C. Bulk Modulus III. $-\frac{1}{\Delta P} (\frac{\Delta V}{V})$ D. Poisson's Ratio IV. $-P(\frac{V}{\Delta V})$
Choose the correct answer from the options given below :
Physics Properties Matching Solution
This question requires matching physical properties of materials (List I) with their corresponding mathematical expressions (List II).
Matching Process:
- A. Young's Modulus: Represents stiffness, defined as longitudinal stress divided by longitudinal strain. The formula is $E = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L} = \frac{FL}{A(\Delta L)}$. This matches expression II.
- B. Compressibility: Defined as the relative change in volume per unit increase in pressure. It is the inverse of Bulk Modulus. The formula is $\beta = -\frac{1}{V} (\frac{\Delta V}{\Delta P})$. Expression III, $-\frac{1}{\Delta P} (\frac{\Delta V}{V})$, is equivalent to this.
- C. Bulk Modulus: Measures resistance to uniform compression. It's defined as the ratio of pressure change to the relative volume change: $K = -\frac{\Delta P}{(\Delta V/V)} = -\frac{V(\Delta P)}{\Delta V}$. Expression IV, $-P(\frac{V}{\Delta V})$, represents this quantity, possibly under the assumption that $\Delta P \approx P$.
- D. Poisson's Ratio: The ratio of transverse strain to axial strain. Mathematically, $\nu = -\frac{\epsilon_{transverse}}{\epsilon_{axial}} = -\frac{(\Delta d/d)}{(\Delta L/L)} = -\frac{\Delta d}{\Delta L}(\frac{L}{d})$. Expression I, $\frac{\Delta d}{\Delta L} (\frac{L}{d})$, matches this, potentially omitting the negative sign common in the definition.
Conclusion
Based on the standard definitions and common representations in physics problems:
- Young's Modulus (A) matches with II.
- Compressibility (B) matches with III.
- Bulk Modulus (C) matches with IV.
- Poisson's Ratio (D) matches with I.
Therefore, the correct matching is A-II, B-III, C-IV, D-I.
This corresponds to Option 1.
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