List - I List - II A. Young's Modulus I. $\frac{-\text{V}\text{d}\text{P}}{\text{d}\text{V}}$ B. Bulk Modulus II. $\frac{-\Delta\text{d}/\text{d}}{\Delta\text{L}/\text{L}}$ C. Modulus of Rigidity III. $\frac{\text{FL}}{\text{A}\Delta\text{L}}$ D. Poisson Ratio IV. $\frac{\text{F}/\text{A}}{x/h}$
Choose the correct answer from the options given below :
Elasticity Concepts Matching
This question requires matching different elastic moduli and Poisson's ratio with their defining mathematical expressions.
Matching List I with List II
A. Young's Modulus
Young's Modulus measures the stiffness of a material under tensile or compressive stress. It is defined as the ratio of longitudinal stress to longitudinal strain.
Formula: $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L}$
This corresponds to term III.
B. Bulk Modulus
Bulk Modulus quantifies a substance's resistance to uniform compression. It is the ratio of pressure change to the relative volume change.
Formula: $B = -\frac{\Delta P}{\Delta V / V}$ or in differential form $B = \frac{-\text{V dP}}{\text{dV}}$
This corresponds to term I.
C. Modulus of Rigidity
The Modulus of Rigidity (or Shear Modulus) describes a solid's resistance to shearing forces. It is the ratio of shear stress to shear strain.
Formula: $G = \frac{\text{Shear Stress}}{\text{Shear Strain}} = \frac{F/A}{x/h}$
This corresponds to term IV.
D. Poisson Ratio
Poisson's Ratio is the ratio of transverse strain (perpendicular to the applied force) to axial strain (parallel to the applied force).
Formula: $\nu = -\frac{\text{Transverse Strain}}{\text{Axial Strain}} = \frac{-\Delta d/d}{\Delta L/L}$
This corresponds to term II.
Correct Match
Based on the definitions:
- A matches with III
- B matches with I
- C matches with IV
- D matches with II
Therefore, the correct matching is A-III, B-I, C-IV, D-II.
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