$A$ 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:

Two wires having the same length and material are stretched by the same force. Their diameters are in the ratio $1:3$. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter),when stretched,is (in $:1$)

$A$ wire is suspended by one end. At the other end,a weight equivalent to $20\, N$ force is applied. If the increase in length is $1.0\, mm$,the ratio of the increase in energy of the wire to the decrease in gravitational potential energy when the load moves downwards by $1\, mm$ will be:

$A$ metal wire of length $L$ is suspended vertically from a rigid support. When a body of mass $M$ is attached to the lower end of the wire,the elongation in the wire is $l$. Consider the following statements:
$(I)$ The loss of gravitational potential energy of mass $M$ is $Mgl$.
$(II)$ The elastic potential energy stored in the wire is $Mgl$.
$(III)$ The elastic potential energy stored in the wire is $\frac{1}{2} Mgl$.
$(IV)$ The heat produced is $\frac{1}{2} Mgl$.
Which of the following statements are correct?

$A$ metal rod of area of cross-section $3 \,cm^2$ is stretched along its length by applying a force of $9 \times 10^4 \,N$. If the Young's modulus of the material of the rod is $2 \times 10^{11} \,Nm^{-2}$, the energy stored per unit volume in the stretched rod is:

$A$ uniform metal rod of $2\, mm^2$ cross-section fixed between two walls is heated from $0\,^oC$ to $20\,^oC$. The coefficient of linear expansion of the rod is $12 \times 10^{-6}/^oC$. Its Young's modulus of elasticity is $10^{11} \,N/m^2$. The energy stored per unit volume of the rod will be ....... $J/m^3$.