The elastic potential energy stored in a copper rod of length $1 \,m$ and area of cross-section $1 \,mm^2$ when stretched by $1 \,mm$ is (Young's modulus of copper $= 1.2 \times 10^{11} \,N/m^2$).

An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is

Work done by the restoring force in a string within the elastic limit is $-10 \, J$. The maximum amount of heat produced in the string is .......... $J$.

$A$ rubber cord catapult has a cross-sectional area of $25\,mm^2$ and an initial length of $10\,cm$. It is stretched by $5\,cm$ and then released to project a missile of mass $5\,g$. Taking $Y_{rubber} = 5 \times 10^8\,N/m^2$,the velocity of the projected missile is ......... $m/s$.

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

$A$ $5 \, m$ long wire is fixed to the ceiling. $A$ weight of $10 \, kg$ is hung at the lower end and is $1 \, m$ above the floor. The wire is elongated by $1 \, mm$. The energy stored in the wire due to stretching is ......... $J$.