The force required to stretch a wire of cross-section $1 \ cm^{2}$ to double its length will be ........ $\times 10^{7} \ N$. (Given Young's modulus of the wire $= 2 \times 10^{11} \ N/m^{2}$)

$A$ 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 ......... $N$ $(\alpha = 10^{-5}/\,^{\circ}C, Y = 2 \times 10^{11}\,N/m^2)$

Two wires of same length having radius of $2 \ mm$ and $1.5 \ mm$ respectively are loaded with same weights. Extension of the second wire is double than that of the first wire. What is the ratio of the Young's modulus of the first wire to that of the second wire?

The density of a rubber cord is $d$. $A$ thick rubber cord of length $L$ and cross-sectional area $A$ undergoes elongation under its own weight when suspended vertically. This elongation is proportional to:

$A$ piece of copper having a rectangular cross-section of $15.2 \; mm \times 19.1 \; mm$ is pulled in tension with $44,500 \; N$ force,producing only elastic deformation. Calculate the resulting strain.

Two wires of equal length and cross-section are suspended as shown. Their Young's moduli are $Y_1$ and $Y_2$ respectively. The equivalent Young's modulus will be