Longitudinal stress of $1\,kg/mm^2$ is applied on a wire. The percentage increase in length is $(Y = 10^{11}\,N/m^2)$. (in $\%$)

The Young's modulus of a wire of length $L$ and radius $r$ is $Y \, N/m^2$. What will be the Young's modulus of a wire made of the same material with length $L/2$ and radius $r/2$?

Consider the situation shown in the figure. The force $F$ is equal to $m_2g/2$. If the area of cross-section of the string is $A$ and its Young's modulus is $Y$,find the strain developed in it. The string is light and there is no friction anywhere.

The following four wires are made of the same material. Which one will have the largest elongation when subjected to the same tension?

Which material has a higher Young's modulus: copper or steel?

$A$ sphere of mass $2 \,kg$ and diameter $4.5 \,cm$ is attached to the lower end of a steel wire of $2 \,m$ length and area of cross-section $0.24 \times 10^{-6} \,m^2$. The wire is suspended from a $205 \,cm$ high ceiling of a room. When the system is made to oscillate as a simple pendulum, the sphere just grazes the floor at its lowest position. Find the velocity of the sphere at the lowest position. (Young's modulus of steel $= 2 \times 10^{11} \,Nm^{-2}$ and acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-1}$)