Two similar wires under the same load yield elongations of $0.1 \ mm$ and $0.05 \ mm$ respectively. If the area of cross-section of the first wire is $4 \ mm^2$,then the area of cross-section of the second wire is..... $mm^2$.

Two different wires made with the same material have their radii in the ratio $1:2$. Their lengths are also in the ratio $1:2$. If the extensions produced are equal when subjected to different loads,find the ratio of the loads applied.

The decrease in length of a metal bar of length $L$ and cross-sectional area $A$ when compressed with a load $F$ along its length is (where $Y$ is Young's modulus of the material of the metal bar).

$A$ metal wire with circular cross-section and length $1 \,m$ is pulled with a tensile force of $1000 \,N$ on each side. For the wire to be stretched not more than $0.25 \,cm$, the minimum diameter of the wire required is (Young's modulus of the metal $= 10^{11} \,Pa$, take $\sqrt{\pi} = 1.77$). (in $\,mm$)

The mean distance between the atoms of iron is $3 \times 10^{-10} \ m$ and the interatomic force constant for iron is $7 \ N/m$. The Young's modulus of elasticity for iron is:

Two wires of equal length and cross-section are suspended as shown. Their Young's moduli are $Y_1$ and $Y_2$ respectively. The equivalent Young's modulus will be