Which of the following statements is correct

A steel wire of cross-sectional area $3\,\, imes \,\,{10^{ - 6}}\,{{\rm{m}}^2}$ can withstand a maximum strain of ${10^{ - 3}}$ . Young’s modulus of steel is $2 imes \,\,{10^{11}}\,{\rm{N}}{{\rm{m}}^{ - 2}}$. The maximum mass the wire can hold is $\left( {{\rm{take}}\,\,\,\,{\rm{g}} = 10{\mkern 1mu} {\mkern 1mu} {\rm{m}}{{\rm{s}}^{ - 2}}} \right)$

A wire of length $L$ and cross-sectional area $A$ stretches by $\Delta L$ under a tensile stress $\sigma$. What is the Young's modulus of the wire?

Two cylinders of the same material and equal volume have cross-sectional areas $A$ and $4A$. If a force $F$ stretches the first cylinder by $\Delta l$, what force is needed to stretch the second cylinder by $2\Delta l$?

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

The mean distance between the atoms of iron is $3 imes {10^{ - 10}}\,m$ and interatomic force constant for iron is $7\,N/m$. The Young’s modulus of elasticity for iron is

A steel wire of length ${\rm{20}}\,\,{\rm{cm}}$ and uniform cross-section ${\rm{1}}\,\,{\rm{m}}{{\rm{m}}^2}$ is tied rigidly at both the ends. The temperature of the wire is altered from ${40^0}C\,\,{\rm{to}}\,\,{20^0}C$. Coefficient of linear expansion of steel is $\alpha = 1.1 imes {10^{ - 5}}^0{C^{ - 1}}$ and $Y$ for steel is $2.0\,\, imes {10^{11}}\,{\rm{N}}{{\rm{m}}^{ - 2}}$; the tension in the wire is

A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to

The elastic limit of a certain material is half its Young's modulus. A wire made of this material, initially 0.5 m long, is stretched to its elastic limit. What is the elongation of the wire?

A rectangular bar $2\,\,cm$ in breadth and $1\,\,cm$ in depth and $100\,\,cm$ in length is supported at its ends and a load of $2$ kg is applied at its middle. If Young’s modulus of the material of the bar is $20\,\, imes \,\,{10^{11}}\,\,{\rm{dyne c}}{{\rm{m}}^{ - 2}},$, the depression in the bar is

A work of $2 imes {10^{ - 2}}J$ is done on a wire of length ${\rm{50}}\,\,{\rm{cm}}$ and area of cross-section ${\rm{0}}{\rm{.5}}\,\,{\rm{m}}{{\rm{m}}^2}$. If the Young’s modulus of the material of the wire is $2\,\, imes \,\,{10^{10}}\,{\rm{N}}{{\rm{m}}^{ - 2}}$ , then the wire must be