$A$ uniform rod of mass $m$,length $L$,area of cross-section $A$ and Young's modulus $Y$ hangs from the ceiling. Its elongation under its own weight will be

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:

$A$ steel wire of length $4.7\; m$ and cross-sectional area $3.0 \times 10^{-5}\; m^{2}$ stretches by the same amount as a copper wire of length $3.5\; m$ and cross-sectional area of $4.0 \times 10^{-5}\; m^{2}$ under a given load. What is the ratio of the Young's modulus of steel to that of copper?

If in case $A$,the elongation in a wire of length $L$ is $l$,then for the same wire,the elongation in case $B$ will be:

The ratio of the lengths of two wires of the same material is $1:2$ and the ratio of their radii is $1:\sqrt{2}$. If they are stretched by the same force,what is the ratio of the increase in their lengths?

$A$ metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{\circ} C$. What is the force required to prevent the expansion of the rod lengthwise? ($Y=$ Young's modulus of the material of the rod,$\alpha=$ coefficient of linear expansion of the rod.)