Two wires $A$ and $B$ of the same material have radii in the ratio $2:1$ and lengths in the ratio $4:1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is .......

Two exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is $2 \,cm$,then how much is the elongation in steel and copper wire respectively? Given,$Y_{\text{steel}} = 20 \times 10^{11} \,dyne/cm^2$,$Y_{\text{copper}} = 12 \times 10^{11} \,dyne/cm^2$.

$A$ 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 $1 \times 10^{12} \,dynes/cm^{2}$]

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

The elongation of the copper wire of cross-sectional area $3.5 \,mm^2$, as shown in the figure, is (Given: $Y_{\text{copper}} = 10 \times 10^{10} \,N/m^2$ and $g = 10 \,m/s^2$).

$A$ wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $F$,its length increases by $5\,cm$. Another wire of the same material of length $4L$ and radius $4r$ is pulled by a force $4F$ under the same conditions. The increase in length of this wire is $....cm$.