JEE Main 2025 — Mechanical Properties of Solids Question with Solution

Two slabs with square cross section of different materials $(1,2)$ with equal sides $(l)$ and thickness ${\mathrm{d}}_1$ and ${\mathrm{d}}_2$ such that ${\mathrm{d}}_2=2{\mathrm{d}}_1$ and $l>{\mathrm{d}}_2$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is ${\theta }_2=2{\theta }_1$. If the shear moduli of material 1 is $4\times 10^9\mathrm{N}/{\mathrm{m}}^2$, then shear moduli of material 2 is $\mathrm{x}\times 10^9\mathrm{N}/{\mathrm{m}}^2$, where value of $x$ is ________.