Young's modulus of a perfectly rigid body material is

$A$ steel wire of length $4.7\; m$ and cross-sectional area $3.0 \times 10^{-5}\; m^{2}$ stretches by the same amount as a copper wire of length $3.5\; m$ and cross-sectional area of $4.0 \times 10^{-5}\; m^{2}$ under a given load. What is the ratio of the Young's modulus of steel to that of copper?

$A$ copper wire of length $1.0\, m$ and a steel wire of length $0.5\, m$ having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by $1\, mm$. If the Young's moduli of copper and steel are respectively $1.0 \times 10^{11}\, N/m^2$ and $2.0 \times 10^{11}\, N/m^2$,the total extension of the composite wire is ........ $mm$.

$A$ steel wire of length $20 \text{ cm}$ and area of cross-section $1 \text{ mm}^2$ is tied rigidly at both the ends. When the temperature of the wire is changed from $40^{\circ} \text{C}$ to $20^{\circ} \text{C}$, find the change in its tension. Given, the coefficient of linear expansion for steel is $\alpha = 1.1 \times 10^{-5} {}^{\circ} \text{C}^{-1}$ and Young's modulus of steel is $Y = 2.0 \times 10^{11} \text{ N/m}^2$. (in $\text{ N}$)

The dimensional formula for Young's modulus is

$A$ horizontal steel railroad track has a length of $100 \, m$ when the temperature is $25^{\circ} C$. The track is constrained from expanding or bending. The stress on the track on a hot summer day,when the temperature is $40^{\circ} C$,is ............. $\times 10^7 \, Pa$. (Note: The linear coefficient of thermal expansion for steel is $1.1 \times 10^{-5} /^{\circ} C$ and the Young's modulus of steel is $2 \times 10^{11} \, Pa$.)