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 …

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)

[JEE Main 2026, 2 Apr (Shift 1)]