$A$ steel wire is $1 \,m$ long and $1 \,mm^2$ in area of cross-section. If it takes $200 \,N$ to stretch this wire by $1 \,mm$,how much force will be required to stretch a wire of the same material as well as diameter from its normal length of $10 \,m$ to a length of $1002 \,cm$?

$A$ wire extends by $1 \ mm$ when a force is applied. If double the force is applied to another wire of the same material and length but half the radius of the cross-section,what will be the elongation of the wire in $mm$?

$A$ block of weight $100 \ N$ is suspended by copper and steel wires of same cross-sectional area $0.5 \ cm^2$ and lengths $\sqrt{3} \ m$ and $1 \ m$,respectively. Their other ends are fixed on a ceiling as shown in the figure. The angles subtended by the copper and steel wires with the ceiling are $30^{\circ}$ and $60^{\circ}$,respectively. If the elongation in the copper wire is $\Delta \ell_C$ and the elongation in the steel wire is $\Delta \ell_S$,then the ratio $\frac{\Delta \ell_C}{\Delta \ell_S}$ is. . . . . .
[Young's modulus for copper and steel are $1 \times 10^{11} \ N/m^2$ and $2 \times 10^{11} \ N/m^2$ respectively]

$A$ mild steel wire of length $1.0 \; m$ and cross-sectional area $0.50 \times 10^{-2} \; cm^{2}$ is stretched,well within its elastic limit,horizontally between two pillars. $A$ mass of $100 \; g$ is suspended from the mid-point of the wire. Calculate the depression at the midpoint.

When a load $W$ is hung from a wire of length $2L$,it just breaks. Now this wire is completely melted and a new wire of length $L$ is formed. If the load $W$ is hung from this new wire,what happens?

The cross-sectional area of all wires is $10^{-4} \ m^2$. What is the displacement of point $D$?