JEE Main 2025 Apr 2 Shift 1, Physics Q22: Properties of Solids

Step 1: Longitudinal strain from Poisson's ratio.

$$\nu =-\frac{{\epsilon }_{\text{transverse}}}{{\epsilon }_{\text{longitudinal}}}$$

Taking magnitudes:

$${\epsilon }_{\ell }=\frac{|{\epsilon }_{\text{transverse}}|}{\nu }=\frac{10^{-3}}{0.2}=5\times 10^{-3}$$

Step 2: Elastic energy density. For Hookean behaviour the strain energy per unit volume is:

$$u=\frac{1}{2}Y{\epsilon }_{\ell }^2$$

$$u=\frac{1}{2}\times 2.0\times 10^{11}\times (5\times 10^{-3}{)}^2$$

$$u=1.0\times 10^{11}\times 25\times 10^{-6}=25\times 10^5{\text{J/m}}^3$$

$\therefore$ The required integer value is $25$.