If the ratio of length,radii,and Young's modulus of steel and aluminium wire are $a, b, c$ respectively,then the corresponding ratio of increase in their length would be:

Young's modulus of a material has the same units as

When a load $W$ is hung from a wire of length $2L$,it just breaks. Now this wire is completely melted and a new wire of length $L$ is formed. If the load $W$ is hung from this new wire,what happens?

$A$ rod is fixed between two points at $20\,^oC$. The coefficient of linear expansion of the material of the rod is $1.1 \times 10^{-5}/\,^oC$ and Young's modulus is $1.2 \times 10^{11}\,N/m^2$. Find the stress developed in the rod if the temperature of the rod becomes $10\,^oC$.

$A$ steel and a brass wire, each of length $50 \,cm$ and cross-sectional area $0.005 \,cm^{2}$, hang from a ceiling and are $15 \,cm$ apart. Lower ends of the wires are attached to a light horizontal bar. $A$ suitable downward load is applied to the bar so that each of the wires extends in length by $0.1 \,cm$. At what distance from the steel wire must the load be applied (in $\,cm$)? [Young's modulus of steel is $2 \times 10^{12} \,dynes/cm^{2}$ and that of brass is $1 \times 10^{12} \,dynes/cm^{2}$]

The length of a metallic wire is $l$. The tension in the wire is $T_1$ for length $l_1$ and the tension in the wire is $T_2$ for length $l_2$. Find the original length $l$.