Young's modulus of a perfectly rigid body material is

$A$ steel rod of radius $20 \ mm$ and length $2 \ m$ is acted upon by a force of $400 \ kN$ along its length. The values of stress and strain are respectively $(Y_{\text{steel}} = 2 \times 10^{11} \ N \ m^{-2})$.

In an experiment to determine the Young's modulus of a wire of length exactly $1\;m$,the extension in the length of the wire is measured as $0.4\;mm$ with an uncertainty of $\pm 0.02\;mm$ when a load of $1\;kg$ is applied. The diameter of the wire is measured as $0.4\;mm$ with an uncertainty of $\pm 0.01\;mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\;N/m^2$. The value of $x$ is (Take $g = 10\;m/s^2$)

When a rod is heated but prevented from expanding,the stress developed is independent of

$A$ steel rod with $Y = 2.0 \times 10^{11} \, N/m^2$ and $\alpha = 10^{-5} \, ^\circ C^{-1}$ of length $4 \, m$ and area of cross-section $10 \, cm^2$ is heated from $0^\circ C$ to $400^\circ C$ without being allowed to extend. The tension produced in the rod is $x \times 10^5 \, N$ where the value of $x$ is ....... .

Stress required in a wire to produce $0.1\%$ strain is $4 \times 10^8 \, N/m^2$. Its Young's modulus is $Y_1$. If stress required in another wire to produce $0.3\%$ strain is $6 \times 10^8 \, N/m^2$,and its Young's modulus is $Y_2$,which relation is correct?