When a uniform wire of radius $r$ is stretched by a $2 \, kg$ weight,the increase in its length is $2.00 \, mm$. If the radius of the wire is $r/2$ and other conditions remain the same,the increase in its length is .......... $mm$. (in $.00$)

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

The length of an iron wire is $L$ and the area of cross-section is $A$. The increase in length is $l$ upon applying a force $F$ on its two ends. Which of the following statements is correct?

If the temperature of a wire of length $2 \,m$ and area of cross-section $1 \,cm^2$ is increased from $0^{\circ}C$ to $80^{\circ}C$ and is not allowed to increase in length,then the force required for it is ............$N$ $\{Y=10^{10} \,N/m^2, \alpha=10^{-6}/^{\circ}C\}$

$A$ cylindrical rod made of aluminum has a length of $1 \,m$ and a diameter of $10 \,cm$. The rod is subjected to a tensile force of $100 \,kN$. Calculate the elongation in the rod. (Young's modulus of aluminum $= 70 \,GPa$)

One end of a steel rod of radius $10.0 \ mm$ and length $50.0 \ cm$ is clamped on a horizontal table. The other end of the rod is pulled with a force of magnitude $10.0 \times \pi \ kN$. This force is uniform across the flat surface of the rod and is perpendicular to it. The change in the length of the rod due to this applied force is (Use Young's modulus $= 2.0 \times 10^{11} \ N/m^2$) (in $mm$)