A wire of length L and cross-sectional area A is stretched by a force F. If the Young's modulus of the material is Y, which of the following expressions correctly represents the strain energy stored in the wire?

A wire of length $2\,\,m$ is made from $10\,\,c{m^3}$ of copper. A force $F$ is applied so that its length increases by $2\,\,mm$. Another wire of length $8\,\,m$ is made from the same volume of copper. If the force $F$ is applied to it, its length will increase by

A force $F$ is required to break a wire of length $I$ and radius $r$. What force is required to break a wire, of the same material, having twice the length and six times the radius ?

If the compressibility of water is $\sigma$ per unit atmospheric pressure, then the decrease in volume ($V$)  due to p, atmospheric pressure will be :

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 pieces of wire $A{\mkern 1mu} {\mkern 1mu} \,and\,B$ of the same material have their lengths in the ratio ${\rm{1 : 2}}$, and their diameters are in the ratio ${\rm{2 : 1}}$. If they are stretched by the same force, their elongations will be in the ratio

Two wires of equal cross-section but one made of steel and the other of copper are joined end to end. When the combination is kept under tension, the elongations in the two wires are found to be equal. What is the ratio of the lengths of the two wires? (Given : steel = $2\,\, imes \,\,{10^{11}}\,{\rm{N}}{{\rm{m}}^{ - 2}})$

What should be the lengths of a steel and copper rod at 0$^ \circ C$  so that the length of the steel rod is 5 cm longer than the copper rod at any temperature?$\alpha$ (Steel) = 1.1$imes {10^{ - 5}}^ \circ {C^{ - 1}}$ $\alpha ($Copper)= $1.7 imes {10^{ - 5}}^ \circ {C^{ - 1}}$ 

A metal rod with Young's modulus $0.8 imes 10^{11} \, ext{N} \, ext{m}^{-2}$ and coefficient of thermal expansion $1.5 imes 10^{-5} \, ext{°C}^{-1}$ is clamped at both ends. If its temperature is increased by $60^{\circ} \, ext{C}$, what stress is developed in the rod?

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

Which of the following statements is correct