Mechanical Properties of Solids

Under the elastic limit, the maximum permissible stress = $8\times10^8\,\mathrm{N/m^2}$. Since

$$\text{strain} \;=\;\frac{\text{stress}}{Y}, \quad \Delta L \;=\;\text{(strain)}\times L,$$

we get

${\mathrm{\Delta L}}_{\max }=\left(\frac{8\times {10}^8}{2\times {10}^{11}}\right)\times 1\mathrm{m}=4\times {10}^{-3}\mathrm{m}=4\mathrm{m}\mathrm{m}\mathrm{.}$

Young’s Modulus

Y = FL / A(ΔL)

So, A → II

Compressibility = 1 / (Bulk modulus)

So, B → III

Bulk Modulus = −P(V/ΔV)

So, C → IV

Poisson’s ratio = (Δd/d) / (ΔL/L)

= (Δd/ΔL) × (L/d)

So, D → I