$A$ rod is fixed between two points at $20\,^oC$. The coefficient of linear expansion of the material of the rod is $1.1 \times 10^{-5}/\,^oC$ and Young's modulus is $1.2 \times 10^{11}\,N/m^2$. Find the stress developed in the rod if the temperature of the rod becomes $10\,^oC$.

$A$ 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

$A$ 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

$A$ wire of length $0.5 \ m$ and area of cross-section $4 \times 10^{-6} \ m^2$ at a temperature of $100^{\circ} C$ is suspended vertically by fixing its upper end to the ceiling. The wire is then cooled to $0^{\circ} C$,but is prevented from contracting,by attaching a mass at the lower end. If the mass of the wire is negligible,then the value of the mass attached to the wire is (Young's modulus of material of the wire $= 10^{11} \ N \ m^{-2}$; coefficient of linear expansion of the material of the wire $= 10^{-5} \ K^{-1}$ and acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $kg$)

Two wires $A$ and $B$ of the same cross-section are connected end to end. When the same tension is applied to both wires,the elongation in wire $B$ is twice the elongation in wire $A$. If $L_A$ and $L_B$ are the initial lengths of the wires $A$ and $B$ respectively,then (Young's modulus of material of wire $A = 2 \times 10^{11} \ Nm^{-2}$ and Young's modulus of material of wire $B = 1.1 \times 10^{11} \ Nm^{-2}$):

If Young's modulus of iron is $2 \times 10^{11} \ N/m^2$ and the interatomic spacing between two molecules is $3 \times 10^{-10} \ m$,the interatomic force constant is ......... $N/m$.