Match List I with List II:

List I	List II
A. Young's Modulus	I. (Δ d)/(Δ L) ( (L)/(d) )$\frac{\Delta d}{\Delta L} \left( \frac{L}{d} \right)$
B. Compressibility	II. (FL)/(A(Δ L))$\frac{FL}{A(\Delta L)}$
C. Bulk Modulus	III. -(1)/(Δ P) ( (Δ V)/(V) )$-\frac{1}{\Delta P} \left( \frac{\Delta V}{V} \right)$
D. Poisson's Ratio	IV. -P ( (V)/(Δ V) )$-P \left( \frac{V}{\Delta V} \right)$

Choose the correct answer from the options given below:

Core Logic

Match the elastic properties to their mathematical definitions:

A. Young's Modulus = Longitudinal StressLongitudinal Strain = (F/A)/(Δ L/L) = (FL)/(AΔ L)$\frac{\text{Longitudinal Stress}}{\text{Longitudinal Strain}} = \frac{F/A}{\Delta L/L} = \frac{FL}{A\Delta L}$ (Matches II)

C. Bulk Modulus = -(Δ P)/(Δ V/V) = -P((V)/(Δ V))$-\frac{\Delta P}{\Delta V/V} = -P\left(\frac{V}{\Delta V}\right)$ (Matches IV)

B. Compressibility = 1Bulk Modulus = -(1)/(Δ P)((Δ V)/(V))$\frac{1}{\text{Bulk Modulus}} = -\frac{1}{\Delta P}\left(\frac{\Delta V}{V}\right)$ (Matches III)

D. Poisson's Ratio = Lateral StrainLongitudinal Strain = (Δ d/d)/(Δ L/L) = (Δ d)/(Δ L)((L)/(d))$\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}} = \frac{\Delta d/d}{\Delta L/L} = \frac{\Delta d}{\Delta L}\left(\frac{L}{d}\right)$ (Matches I)

Step 1: Final Conclusion

A arrow$\rightarrow$ II B arrow$\rightarrow$ III C arrow$\rightarrow$ IV D arrow$\rightarrow$ I

Pattern Recognition

Compressibility is always the reciprocal of Bulk Modulus. Identifying Poisson's ratio as the only formula with diameter 'd$d$' makes solving instant.

Chapter Mix

Class 11 Physics: Mechanical Properties of Solids