The Young's modulus of a wire of length $L$ and radius $r$ is $Y$. If the length is reduced to $\frac{L}{2}$ and radius is $\frac{r}{2}$,then the Young's modulus will be

Two wires of diameter $0.25 \; cm,$ one made of steel and the other made of brass,are loaded as shown in the figure. The unloaded length of the steel wire is $1.5 \; m$ and that of the brass wire is $1.0 \; m.$ Compute the elongations of the steel and the brass wires. (Given: Young's modulus of steel $Y_s = 2.0 \times 10^{11} \; Pa,$ Young's modulus of brass $Y_b = 0.91 \times 10^{11} \; Pa$)

What is the percentage increase in length of a wire of diameter $2.5 \,mm$,stretched by a force of $100 \,kg$ wt? (Young's modulus of elasticity of wire $= 12.5 \times 10^{11} \,dyne/cm^2$)

$A$ metallic rod breaks when the strain produced is $0.2 \%$. The Young's modulus of the material of the rod is $7 \times 10^9 \,N/m^2$. The area of cross-section required to support a load of $10^4 \,N$ is:

Increase in length of a wire is $1 \, mm$ when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius,the increase in length will be ........ $mm$.

$A$ structural steel rod has a radius of $10\,mm$ and length of $1.0\,m.$ $A$ $100\,kN$ force stretches it along its length. Young's modulus of structural steel is $2 \times 10^{11}\,N/m^2.$ The percentage strain is about ....... $\%$