The work done in stretching an elastic wire per unit volume is

When a force is applied on a wire of uniform cross-sectional area $3 \times 10^{-6} \, m^2$ and length $4 \, m$,the increase in length is $1 \, mm$. The energy stored in it will be $(Y = 2 \times 10^{11} \, N/m^2)$. (in $, J$)

The length of a rod is $20 \, cm$ and the area of cross-section is $2 \, cm^2$. The Young's modulus of the material of the rod is $1.4 \times 10^{11} \, N/m^2$. If the rod is compressed by a force of $5 \, kg-wt$ along its length,then the increase in the elastic potential energy of the rod in joules will be:

The work done on a wire of volume $2 \,cm^3$ is $16 \times 10^2 \,J$. If the Young's modulus of the material of the wire is $4 \times 10^{12} \,N/m^2$, then the strain produced in 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:

If the force constant of a wire is $K$,the work done in increasing the length of the wire by $l$ is