The maximum elongation of a steel wire of $1 \,m$ length if the elastic limit of steel and its Young's modulus,respectively,are $8 \times 10^8 \,N \,m^{-2}$ and $2 \times 10^{11} \,N \,m^{-2}$,is: (in $\,mm$)

An aluminum rod (Young's modulus $Y = 7 \times 10^9 \, N/m^2$) has a breaking strain of $0.2\%$. The minimum cross-sectional area of the rod required to support a load of $10^4 \, N$ is:

$A$ weight of $200 \, kg$ is suspended by a vertical wire of length $600.5 \, cm$. The area of cross-section of the wire is $1 \, mm^2$. When the load is removed,the wire contracts by $0.5 \, cm$. The Young's modulus of the material of the wire will be:

When a weight of $10 \,kg$ is suspended from a copper wire of length $3 \,m$ and diameter $0.4 \,mm$, its length increases by $2.4 \,cm$. If the diameter of the wire is doubled, then the extension in its length will be (in $\,cm$)

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 ............$N$ $\{Y=10^{10} \,N/m^2, \alpha=10^{-6}/^{\circ}C\}$

$A$ wire of length $0.5 \ m$ and area of cross-section $4 \times 10^{-6} \ m^2$ at a temperature of $100^{\circ} C$ is suspended vertically by fixing its upper end to the ceiling. The wire is then cooled to $0^{\circ} C$,but is prevented from contracting,by attaching a mass at the lower end. If the mass of the wire is negligible,then the value of the mass attached to the wire is (Young's modulus of material of the wire $= 10^{11} \ N \ m^{-2}$; coefficient of linear expansion of the material of the wire $= 10^{-5} \ K^{-1}$ and acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $kg$)