$A$ wire of cross-section $4 \; mm^2$ is stretched by $0.1 \; mm$ by a certain weight. How far (length) will a wire of the same material and length but of area $8 \; mm^2$ stretch under the action of the same force?

The following four wires are made of the same material. If the same tension is applied to each,the wire having the largest extension is

On applying a stress of $20 \times 10^8 \ N/m^2$,the length of a perfectly elastic wire is doubled. Its Young's modulus will be:

$A$ 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 $1 \times 10^{12} \,dynes/cm^{2}$]

Two separate wires $A$ and $B$ are stretched by $2 \, mm$ and $4 \, mm$ respectively,when they are subjected to a force of $2 \, N$. Assume that both the wires are made up of the same material and the radius of wire $B$ is $4$ times that of the radius of wire $A$. The lengths of the wires $A$ and $B$ are in the ratio of $a : b$. Then $a / b$ can be expressed as $1 / x$ where $x$ is:

Four wires of the same material are stretched by the same load. Which one of them will elongate the most if their dimensions are as follows?