$A$ 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?

Four identical hollow cylindrical columns of mild steel support a big structure of mass $50,000 \; kg$. The inner and outer radii of each column are $30 \; cm$ and $60 \; cm$ respectively. Assuming the load distribution to be uniform,calculate the compressional strain of each column. (Take Young's modulus of mild steel $Y = 2.0 \times 10^{11} \; Pa$ and $g = 9.8 \; m/s^2$)

$A$ rod of length $l$ and area of cross-section $A$ is heated from $0^{\circ}C$ to $100^{\circ}C$. The rod is so placed that it is not allowed to increase in length,then the force developed is proportional to

Three bars having lengths $l, 2l$,and $3l$ and areas of cross-section $A, 2A$,and $3A$ are joined rigidly end to end. The compound rod is subjected to a stretching force $F$. The total increase in the length of the rod is (Young's modulus of the material is $Y$ and the bars are massless).

$A$ $0.1 \,kg$ mass is suspended from a wire of negligible mass. The length of the wire is $1 \,m$ and its cross-sectional area is $4.9 \times 10^{-7} \,m^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140 \,rad \,s^{-1}$. If the Young's modulus of the material of the wire is $n \times 10^9 \,N \,m^{-2}$, the value of $n$ is

$A$ 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 $kg$)