Young's modulus of the material of a wire of length $L$ and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and the cross-sectional area is halved,then the Young's modulus will be:

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 $...... \, \mu m$.

The area of cross-section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} \, m^2$. The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to $25$ metric tons,the required area of cross-section of the rope should be $......... \times 10^{-4} \, m^2$ (take $g = 10 \, m/s^2$).

$A$ copper wire of length $2.2 \; m$ and a steel wire of length $1.6 \; m$,both of diameter $3.0 \; mm$,are connected end to end. When stretched by a load,the net elongation is found to be $0.70 \; mm$. Obtain the load applied in $N$.

$A$ $3 \ m$ long wire of radius $3 \ mm$ shows an extension of $0.1 \ mm$ when loaded vertically by a mass of $50 \ kg$ in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is $P \times 10^{11} \ Nm^{-2}$,where the value of $P$ is: (Take $g = 3 \pi \ m/s^2$)

$A$ steel wire is stretched with a definite load. If the Young's modulus of the wire is $Y$,how can the value of $Y$ be decreased?