If the interatomic spacing in a steel wire is $3.0 \mathring{A}$ and $Y_{\text{steel}} = 20 \times 10^{10} \text{ N/m}^2$, then the force constant is:

$A$ rod of length $L$ and radius $r$ is held between two rigid walls so that it is not allowed to expand. If its temperature is increased,then the force developed in it is proportional to .........

$A$ stretched wire of a material whose Young's modulus $Y = 2 \times 10^{11} \ Nm^{-2}$ has Poisson's ratio $\sigma = 0.25$. Its lateral strain is $\varepsilon_l = 10^{-3}$. The elastic energy density of the wire is:

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 $B = 1.1 \times 10^{11} \ Nm^{-2}$):

$A$ copper wire of length $2.4 \ m$ and an aluminum wire of length $0.7 \ m$, both having diameter $2 \ mm$, are connected end to end. When stretched by a load, the total elongation is found to be $0.6 \ mm$. The applied load is (Young's modulus of copper $= 1.2 \times 10^{11} \ N/m^2$ and Young's modulus of aluminum $= 0.7 \times 10^{11} \ N/m^2$). (in $\pi \ N$)

There is some change in length when a $33000 \,N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} \,m^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is $3 \times 10^{11} \,N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ}C$). (in $^{\circ}C$)