Four identical rods are stretched by the same force. The maximum extension is produced in:

How much force is required to produce an increase of $0.2\%$ in the length of a brass wire of diameter $0.6\, mm$ (Young's modulus for brass = $0.9 \times 10^{11} \, N/m^2$)?

$A$ steel rod of radius $20 \ mm$ and length $2 \ m$ is acted upon by a force of $400 \ kN$ along its length. The values of stress and strain are respectively $(Y_{\text{steel}} = 2 \times 10^{11} \ N \ m^{-2})$.

$A$ 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 $1002 \,cm$?

Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^{3} \; \text{kg}$. The inner and outer radii of each column are $50 \; \text{cm}$ and $100 \; \text{cm}$ respectively. Assuming uniform load distribution,calculate the compressive strain of each column. [Use $Y = 2.0 \times 10^{11} \; \text{Pa}$,$g = 9.8 \; \text{m/s}^2$]

When a wire of length $L$ clamped at one end is pulled by a force $F$ from the other end,its length increases by $l$. If the radius of the wire and the applied force were halved,then the increase in its length is