If the given graph shows the load $(W)$ attached to and the elongation $(\Delta l)$ produced in a wire of length $1 \,m$ and area of cross-section $1 \,mm^2$, then the Young's modulus of the material of the wire is

$A$ block of mass $2 \ kg$ is tied to one end of a $2 \ m$ long metal wire of $1.0 \ mm^2$ area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is $2 \ mm$,the Young's modulus of the metal is (Acceleration due to gravity $= 10 \ ms^{-2}$)

$A$ brass wire $1.8\; m$ long at $27\;^{\circ}C$ is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of $-39\;^{\circ}C$,what is the tension developed in the wire,if its diameter is $2.0\; mm$? (Coefficient of linear expansion of brass $\alpha = 2.0 \times 10^{-5}\; K^{-1}$; Young's modulus of brass $Y = 0.91 \times 10^{11}\; Pa$)

$A$ rod of length $L$ and radius $r$ is held between two rigid walls so that it is not allowed to expand. If its temperature is increased,then the force developed in it is proportional to .........

What force is required to stretch a wire of cross-sectional area $1 \, cm^2$ to $1.1$ times its original length? (Given: Young's modulus $Y = 2 \times 10^{11} \, N/m^2$)

$A$ steel and a brass wire, each of length $50 \,cm$ and cross-sectional area $0.005 \,cm^{2}$, hang from a ceiling and are $15 \,cm$ apart. Lower ends of the wires are attached to a light horizontal bar. $A$ suitable downward load is applied to the bar so that each of the wires extends in length by $0.1 \,cm$. At what distance from the steel wire must the load be applied (in $\,cm$)? [Young's modulus of steel is $2 \times 10^{12} \,dynes/cm^{2}$ and that of brass is $1 \times 10^{12} \,dynes/cm^{2}$]