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 $:1$)

The elastic energy stored in a wire of Young's modulus $Y$ is

$A$ brass rod of cross-sectional area $1 \, cm^2$ and length $0.2 \, m$ is compressed lengthwise by a weight of $5 \, kg$. If Young's modulus of elasticity of brass is $1 \times 10^{11} \, N/m^2$ and $g = 10 \, m/s^2$,then the increase in the energy of the rod will be:

$A$ 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:

$A$ 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 ....... $J/m^3$.

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 $: 1$)