$A$ rod of uniform cross-sectional area $A$ and length $L$ has a weight $W$. It is suspended vertically from a fixed support. If Young's modulus for the rod is $Y$,then the elongation produced in the rod due to its own weight is:

$A$ mild steel wire of length $1.0 \; m$ and cross-sectional area $0.50 \times 10^{-2} \; cm^{2}$ is stretched,well within its elastic limit,horizontally between two pillars. $A$ mass of $100 \; g$ is suspended from the mid-point of the wire. Calculate the depression at the midpoint.

On applying a stress of $20 \times 10^8 \ N/m^2$,the length of a perfectly elastic wire is doubled. Its Young's modulus will be:

$A$ steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^{\circ}C$ so that it cannot contract on cooling. The tension in the rod at $0\,^{\circ}C$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^{\circ}C, Y = 2 \times 10^{11}\,N/m^2)$

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).

$A$ metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If $L$,$\alpha$,and $Y$ denote the length of the rod,the coefficient of linear thermal expansion,and the Young's modulus of its material respectively,then for an increase in temperature of the rod by $\Delta T$,the longitudinal stress developed in the rod is