The figure represents the extension $(\Delta l)$ of a wire of length $1\text{ m}$,suspended from the ceiling of a room at one end with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-5}\text{ m}^2$,then the Young's modulus of the wire is . . . . . . $\text{N/m}^2$.

$A$ student performs an experiment to determine the Young's modulus of a wire of length $2 \, m$ using Searle's method. In an observation,for a load of $10 \, kg$,the extension of the wire is measured as $0.88 \, mm$ with an uncertainty of $\pm 0.05 \, mm$. The student also measures the diameter of the wire as $0.4 \, mm$ with an uncertainty of $\pm 0.01 \, mm$. Take $g = 9.8 \, m/s^2$ (exact). Calculate the Young's modulus of the wire.

Two wires each of radius $0.2\,cm$ and negligible mass, one made of steel and the other made of brass, are loaded as shown in the figure. The elongation of the steel wire is $.........\times 10^{-6}\,m$. [Young's modulus for steel $= 2 \times 10^{11}\,N/m^2$ and $g = 10\,m/s^2$]

Write the unit and dimensional formula of modulus of elasticity.

$A$ 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 units of Young's modulus of elasticity are