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

If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are $a, b$ and $c$ respectively, then the corresponding ratio of increase in their lengths is

A copper wire $(Y = 1 \times 10^{11}\, N/m^2)$ of length $6\, m$ and a steel wire $(Y = 2 \times 10^{11}\, N/m^2)$ of length $4\, m$ each of cross section $10^{-5}\, m^2$ are fastened end to end and stretched by a tension of $100\, N$. The elongation produced in the copper wire is ……… $mm$

On all the six surfaces of a unit cube, equal tensile force of $F$ is applied. The increase in length of each side will be ($Y =$ Young's modulus, $\sigma $= Poission's ratio)

The interatomic distance for a metal is $3 \times {10^{ – 10}}\,m$. If the interatomic force constant is $3.6 \times {10^{ – 9}}\,N/{{\buildrel _{\circ} \over {\mathrm{A}}}}$, then the Young's modulus in $N/{m^2}$ will be