When a force of $4 \, N$ is applied to a wire,its length is $a \, m$. When a force of $5 \, N$ is applied,its length is $b \, m$. What will be its length when a force of $9 \, N$ is applied?

$A$ $5\, m$ long aluminium wire $(Y = 7 \times 10^{10}\, N/m^2)$ of diameter $3\, mm$ supports a $40\, kg$ mass. In order to have the same elongation in a copper wire $(Y = 12 \times 10^{10}\, N/m^2)$ of the same length under the same weight,the diameter should now be,in $mm$.

To break a wire of $1 \, m$ length, a minimum weight of $40 \, kg \, wt$ is required. Then, the wire of the same material with double the radius and $6 \, m$ length will require a breaking weight of ....... $kg \, wt$.

What should be the diameter of a copper wire $(Y=12 \times 10^{10} \text{ N/m}^2)$ of length $5 \text{ m}$ to produce the same elongation produced by a $5 \text{ m}$ long aluminium wire $(Y=7 \times 10^{10} \text{ N/m}^2)$ of diameter $3 \text{ mm}$ with the same $40 \text{ kg}$ mass (in $\text{ mm}$)?

$A$ metallic bar of Young's modulus $0.5 \times 10^{11} \,N \,m^{-2}$, coefficient of linear thermal expansion $10^{-5} \,^{\circ}C^{-1}$, length $1 \,m$, and area of cross-section $10^{-3} \,m^2$ is heated from $0^{\circ}C$ to $100^{\circ}C$ without expansion or bending. The compressive force developed in it is:

The Young's modulus of a wire of length $L$ and radius $r$ is $Y \ N/m^2$. If the length and radius are reduced to $L/2$ and $r/2,$ then its Young's modulus will be