Two wires $A$ and $B$ having same length and material are stretched by the same force. Their diameters are in the ratio $1: 3$. The ratio of energy density of wire $A$ to that of wire $B$ when stretched,is (in $: 1$)

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 of length $1 \, m$ and Young's modulus $Y = 2.0 \times 10^{11} \, N/m^2$ is fixed between two rigid supports. If its temperature is increased by $100 ^\circ C$,what is the energy stored in the wire? (Given: $\alpha = 18 \times 10^{-6} \, ^\circ C^{-1}$,$A = 1 \, cm^2$)

Two wires of the same material and length but diameters in the ratio $1:2$ are stretched by the same force. The elastic potential energy per unit volume for the wires,when stretched by the same force,will be in the ratio: (in $:1$)

Determine the elastic potential energy stored in a stretched wire.

$A$ metal rod has length,cross-sectional area,and Young's modulus as $L$,$A$,and $Y$ respectively. If the elongation produced in the rod is $\ell$,then the work done is proportional to: