When a weight $Mg$ is suspended from a wire of length $L$,the increase in length is $l$ meters. The energy stored in the wire is:

$A$ steel uniform rod of length $2L$,cross-sectional area $A$,and mass $M$ is set rotating in a horizontal plane about an axis passing through its center with angular velocity $\omega$. If $Y$ is the Young's modulus for steel,find the total extension in the length of the rod.

$A$ wire of Young's modulus $1.6 \times 10^{12} \,N/m^{2}$ is stretched by a force so as to produce a strain of $2 \times 10^{-4}$. The energy density of the wire is

$A$ boy's catapult is made of a rubber cord which is $42\, cm$ long,with $6\, mm$ diameter of cross-section and of negligible mass. The boy keeps a stone weighing $0.02\, kg$ on it and stretches the cord by $20\, cm$ by applying a constant force. When released,the stone flies off with a velocity of $20\, m/s$. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to:

$A$ steel rod of length $\ell$,cross-sectional area $A$,Young's modulus of elasticity $Y$,and thermal coefficient of linear expansion $\alpha$ is heated so that its temperature increases by $t\,^\circ C$. The work that can be done by the rod on heating is:

If $x$ longitudinal strain is produced in a wire of Young's modulus $y,$ then energy stored in the material of the wire per unit volume is