The area of a cross-section of a steel wire is $0.1 \, cm^2$ and Young's modulus of steel is $2 \times 10^{11} \, N \, m^{-2}$. The force required to stretch it by $0.1 \%$ of its original length is ......... $N$.

Under the same load,wire $A$ having length $5.0 \, m$ and cross-section $2.5 \times 10^{-5} \, m^2$ stretches uniformly by the same amount as another wire $B$ of length $6.0 \, m$ and a cross-section of $3.0 \times 10^{-5} \, m^2$ stretches. The ratio of the Young's modulus of wire $A$ to that of wire $B$ will be

$A$ steel rail of length $5\,m$ and area of cross-section $40\,cm^2$ is prevented from expanding along its length while the temperature rises by $10\,^{\circ}C$. If the coefficient of linear expansion and Young's modulus of steel are $1.2\times10^{-5}\,K^{-1}$ and $2\times10^{11}\,N/m^2$ respectively,the force developed in the rail is approximately:

Explain the experimental determination of Young's modulus.

What is the effect of change in temperature on the Young's modulus?

What should be the diameter of a copper wire $(Y=12 \times 10^{10} \text{ N/m}^2)$ of length $5 \text{ m}$ to produce the same elongation produced by a $5 \text{ m}$ long aluminium wire $(Y=7 \times 10^{10} \text{ N/m}^2)$ of diameter $3 \text{ mm}$ with the same $40 \text{ kg}$ mass (in $\text{ mm}$)?