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.…

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