$A$ fixed volume of iron is drawn into a wire of length $l$. The extension produced in this wire by a constant force $F$ is proportional to

$A$ student performs an experiment to determine the Young's modulus of a wire, exactly $2 \,m$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 \,mm$ with an uncertainty of $\pm 0.05 \,mm$ at a load of exactly $1.0 \,kg$. The student also measures the diameter of the wire to be $0.4 \,mm$ with an uncertainty of $\pm 0.01 \,mm$. Take $g=9.8 \,m/s^2$ (exact). The Young's modulus obtained from the reading is

$A$ wire of length $2 \ m$ and cross-sectional area $10^{-2} \ cm^2$ is fixed at one end. $A$ force of $200 \ N$ is applied at the other end. The coefficient of linear expansion of the wire is $1.1 \times 10^{-5} \ ^oC^{-1}$ and the Young's modulus is $1.2 \times 10^{11} \ N/m^2$. If the temperature is increased by $10^oC$,what will be the thermal stress developed in the wire?

$A$ 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 $\text{ N}$)

$A$ metallic ring of radius $r$ and cross-sectional area $A$ is fitted into a wooden circular disc of radius $R$ $(R > r)$. If the Young's modulus of the material of the ring is $Y$, the force with which the metal ring expands is

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