$A$ wire of cross-sectional area $10^{-6} \, m^2$ is stretched such that its length increases by $0.1\%$. If the tension produced in the wire is $1000 \, N$, calculate the Young's modulus of the wire.

Two persons pull a wire towards themselves. Each person exerts a force of $200 \, N$ on the wire. Young's modulus of the material of the wire is $1 \times 10^{11} \, N \, m^{-2}$. The original length of the wire is $2 \, m$ and the area of cross-section is $2 \, cm^2$. The wire will extend in length by $...... \, \mu m$.

What is the effect of change in temperature on the Young's modulus?

The units of Young's modulus of elasticity are

$A$ uniform steel rod of mass $1.8 \,kg$ and length $0.8 \,m$ is hung from a nail with the help of two steel wires,each of area of cross-section $0.01 \,mm^2$ and unstretched length $0.5 \,m$,as shown in the figure. The centre of mass of the rod lies vertically below the nail. The increase in the distance between the centre of mass of the rod and the nail due to stretching of the wires as the rod hangs is . . . . . . $mm$. (Young's modulus of steel $= 2 \times 10^{11} \,N/m^2$ and acceleration due to gravity $= 10 \,m/s^2$)

$A$ force $F$ is applied on a wire of radius $r$ and length $L$,and the change in the length of the wire is $l$. If the same force $F$ is applied on a wire of the same material with radius $2r$ and length $2L$,then what is the change in the length of the second wire?