Consider a rod of length $1.0 \ m$ with a cross-sectional area of $0.50 \ cm^2$. The rod supports a $500 \ kg$ platform that hangs attached to the rod's lower end. What is the elongation of the rod under the stress, ignoring the weight of the rod (in $mm$)? Consider Young's modulus to be $10^{11} \ Pa$ and $g = 10 \ m \ s^{-2}$.

The length of a light string is $1.4 \ m$ when the tension on it is $5 \ N$. If the tension increases to $7 \ N$,the length of the string is $1.56 \ m$. The original length of the string is . . . . . . $m$.

The area of cross-section of a wire of length $1.1 \, m$ is $1 \, mm^2$. It is loaded with $1 \, kg$. If Young's modulus of copper is $1.1 \times 10^{11} \, N/m^2$,then the increase in length will be ......... $mm$ (Take $g = 10 \, m/s^2$)

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

Two wires of diameter $0.25 \; cm,$ one made of steel and the other made of brass,are loaded as shown in the figure. The unloaded length of the steel wire is $1.5 \; m$ and that of the brass wire is $1.0 \; m.$ Compute the elongations of the steel and the brass wires. (Given: Young's modulus of steel $Y_s = 2.0 \times 10^{11} \; Pa,$ Young's modulus of brass $Y_b = 0.91 \times 10^{11} \; Pa$)

The Young's modulus of a rubber string $8\, cm$ long and density $1.5\, kg/m^3$ is $5 \times 10^8\, N/m^2$. If it is suspended from the ceiling in a room,the increase in length due to its own weight will be: