The unit of Young's modulus is

$A$ steel ring of radius $r$ and cross-section area $A$ is fitted onto a wooden disc of radius $R$ $(R > r)$. If Young's modulus is $E$,then the force with which the steel ring is expanded is

The decrease in length of a metal bar of length $L$ and cross-sectional area $A$ when compressed with a load $F$ along its length is (where $Y$ is Young's modulus of the material of the metal bar).

$A$ thin $1 \, m$ long rod has a radius of $5 \, mm$. $A$ force of $50 \, \pi \, kN$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is $0.01 \, mm$,which of the following statements is false?

$A$ wire is suspended from a rigid support and a weight $W$ is attached to its free end,causing an extension of $1.0 \, mm$. If the same wire is passed over a pulley and a weight $W$ is attached to each of its two ends,what will be the extension in the wire in $mm$?

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 $g = 10\;m/s^2$)