$A$ wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$,its length increases by $l$. Another wire of the same material of length $2L$ and radius $2r$ is pulled by a force $2f$. Then the increase in its length will be

$A$ load of $1 \,kg$ weight is attached to one end of a steel wire of area of cross-section $3 \,mm^2$ and Young's modulus $10^{11} \,N/m^2$. The other end is suspended vertically from a hook on a wall, then the load is pulled horizontally and released. When the load passes through its lowest position, the fractional change in length is $(g = 10 \,m/s^2)$.

If Young's modulus of iron is $2 \times 10^{11} \ N/m^2$ and the interatomic spacing between two molecules is $3 \times 10^{-10} \ m$,the interatomic force constant is ......... $N/m$.

In the given figure,if the dimensions of the two wires are same but materials are different,then Young's modulus is ........

An iron rod of length $2\, m$ and cross-sectional area of $50\, mm^2$ is stretched by $0.5\, mm$ when a mass of $250\, kg$ is hung from its lower end. The Young's modulus of the iron rod is:

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1\, m$ suspended from the top of a roof at one end and with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6}\, m^2$,calculate the Young's modulus of the material of the wire.