JEE Main 2026 — Mechanical Properties of Solids Question with Solution

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)