$A$ wire of length $100 \ cm$ and area of cross-section $2 \ mm^2$ is stretched by two forces of each $440 \ N$ applied at the ends of the wire in opposite directions along the length of the wire. If the elongation of the wire is $2 \ mm$,the Young's modulus of the material of the wire is:

Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is $0.5 \ cm$,find the elongation $(l)$ of each wire. Given: ${Y_s} = 2.0 \times {10^{11}} \ N/m^2$ and ${Y_c} = 1.2 \times {10^{11}} \ N/m^2$.

$A$ structural steel rod has a radius of $10 \;mm$ and a length of $1.0 \;m$. $A$ $100 \;kN$ force stretches it along its length. Calculate $(a)$ stress,$(b)$ elongation,and $(c)$ strain on the rod. Young's modulus of structural steel is $2.0 \times 10^{11} \;N \;m^{-2}$.

One end of a metal wire is fixed to a ceiling and a load of $2 \ kg$ hangs from the other end. $A$ similar wire is attached to the bottom of the load and another load of $1 \ kg$ hangs from this lower wire. Then the ratio of longitudinal strain of the upper wire to that of the lower wire will be . . . . . . .
[Area of cross section of wire $= 0.005 \ cm^2$,$Y = 2 \times 10^{11} \ Nm^{-2}$ and $g = 10 \ ms^{-2}$]

Copper of fixed volume $V$ is drawn into a wire of length $l$. When this wire is subjected to a constant force $F$,the extension produced in the wire is $\Delta l$. Which of the following graphs is a straight line?

Two metal wires $A$ and $B$ have lengths $L$ and $3L$ respectively. The radii of the cross-sectional circular areas of wires $A$ and $B$ are $R$ and $2R$, respectively. These wires are joined end-to-end along their axis. When one end of the combined system is fixed and the other end is pulled with a constant force $F$, the elongation in both wires is equal. If $Y_A$ and $Y_B$ are the Young's moduli of wires $A$ and $B$, respectively, then the ratio $Y_B / Y_A$ is: