Mechanical Properties of question bank (Physics)

The diameter of a wire measured by a screw gauge of least count $0.001$ cm is $0.08$ cm. The length measured by a scale of least count $0.1$ cm is $150$ cm. When a weight of $100$ N is applied to the wire, the extension in length is $0.5$ cm, measured by a micrometer of least count $0.001$ cm. The error in the measured Young's modulus is $\alpha \times 10^9$ N/m$^2$. The value of $\alpha$ is _______.
(Ignore the contribution of the load to Young's modulus error calculation)

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 $l \gt \mathrm{d}_2$. 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 ________.