A metal wire of Young's modulus $2 imes 10^{11} \, N/m^2$ undergoes a strain of $10^{-3}$. What is the energy stored per unit volume in the wire?

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 wires of the same material have lengths in the ratio ${\rm{1 : 2}}$ and their radii are in the ratio $1{\rm{ }}:\sqrt 2$ If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

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 ratio of diameters of two wires of same materials is $n:1$. The length of each wire is ${\rm{4}}\,\,{\rm{m}}$. On applying the same load, the increase in length of thin wire will be $\left( {n > 1} \right)$

A spring of constant $k$ is cut into parts of length in the ratio ${\rm{1 : 2}}$. The spring constant of larger on is

Consider an iron rod of length $1{\rm{ }}m$ and cross-section ${\rm{1}}\,\,{\rm{c}}{{\rm{m}}^2}$ with a Young’s modulus of ${10^{12}}$ dyne ${\rm{c}}{{\rm{m}}^{ - 2}}$. We wish to calculate the force with which the two ends must be pulled to produce an elongation of $1{\rm{ }}mm$. It is equal to

The radii and Young’s modulii of two uniform wires $A$ and $B$ are in the ratio ${\rm{2:1}}$ and ${\rm{1:2}}$ respectively. Both wires are subjected to the same longitudinal force. If the increase in length of the wire $A$ is one percent, the percentage increase in length of the wire $B$ is

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

A copper wire and a steel wire of the same diameter and length are connected end to end and a force is applied, which stretches their combined length by $1{\rm{ }}cm$. The two wires will have

A steel ring of radius $r$ and cross-sectional area 'A' is fitted onto a wooden disc of radius R(R > r). If Young’s modulus be $E$, then the force with which the steel ring is expanded is