$A$ 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 $\pi \ N$)

$A$ rod of uniform cross-sectional area $A$ and length $L$ has a weight $W$. It is suspended vertically from a fixed support. If Young's modulus for the rod is $Y$,then the elongation produced in the rod due to its own weight is:

Young's modulus of rubber is $10^4 \ N/m^2$ and the area of cross-section is $2 \ cm^2$. If a force of $2 \times 10^5 \ dynes$ is applied along its length,then its initial length $L$ becomes:

The ratio of diameters of two wires of the same material is $n : 1$. The length of each wire is $4 \ m$. On applying the same load,the increase in length of the thin wire will be:

$A$ metal rod of cross-sectional area $3 \times 10^{-6} \,m^{2}$ is suspended vertically from one end and has a length of $0.4 \,m$ at $100^{\circ} C$. The rod is cooled to $0^{\circ} C$, but prevented from contracting by attaching a mass '$m$' at the lower end. Find the value of '$m$'. (Given: $Y = 10^{11} \,N/m^{2}$, coefficient of linear expansion $\alpha = 10^{-5} /K$, $g = 10 \,m/s^{2}$) (in $\,kg$)

$A$ 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?