$A$ wire of length $50\, cm$ and cross-sectional area of $1\, mm^2$ is extended by $1\, mm$. The required work done will be $(Y = 2 \times 10^{10}\, N/m^2)$.

When a load of $5\,kg$ is hung on a wire, an extension of $3\,m$ takes place. The work done will be ....... $Joule$. (Take $g = 10\,m/s^2$)

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

$A$ rubber pipe of density $1.5 \times 10^3 \, kg/m^3$ and Young's modulus $5 \times 10^6 \, N/m^2$ is suspended from the roof. The length of the pipe is $8 \, m$. What will be the change in length due to its own weight?

The length of a wire is $1.0 \, m$ and the area of cross-section is $1.0 \times 10^{-2} \, cm^2$. If the work done for an increase in length by $0.2 \, cm$ is $0.4 \, J$,then the Young's modulus of the material of the wire is:

$A$ uniform heavy rod of weight $10 \, N$,cross-sectional area $100 \, \text{cm}^2$ and length $20 \, \text{cm}$ is hanging from a fixed support. The Young's modulus of the material of the rod is $2 \times 10^{11} \, \text{N/m}^2$. Neglecting the lateral contraction,find the elongation of the rod due to its own weight. (In $\times 10^{-10} \, \text{m}$)