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

A wire suspended vertically from one end is stretched by attaching a weight $200 \,N$ to the lower end. The weight stretches the wire by $1 \,mm$. The elastic potential energy gained by the wire is ....... $J$

An $8\,m$ long copper wire and $4\,m$ long steel wire, each of cross section $0.5\,cm^2$ are fastened end to end and stretched by $500\,N$ force. The elastic potential energy of the system is (Youngs mod $: Y_{cu}= 1\times 10^{11}\,N/m^2,$ $Y_{steel} = 2\times 10^{11}\,N/m^2$ ) :

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 increase in energy of the wire will be .......  $joule$

What is called elastic energy density ? Write its formula and dimensional formula.

A wire of length $L$ and cross-sectional area $A$ is made of a material of Young's modulus $Y.$ It is stretched by an amount $x$. The work done is