$A$ thick rope of density $\rho$ and length $L$ is hung from a rigid support. The Young's modulus of the material of the rope is $Y$. The increase in length of the rope due to its own weight is

$A$ 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

$A$ copper wire of length $3 \text{ m}$ is stretched by $3 \text{ mm}$ by applying an external force. The volume of the wire is $600 \times 10^{-6} \text{ m}^3$. The elastic potential energy stored in the wire in the stretched condition is . . . . . . $\text{J}$. (Given Young's modulus of copper $Y = 1.1 \times 10^{11} \text{ N/m}^2$)

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

When the load applied to a wire is increased from $5 \ kg$ wt to $8 \ kg$ wt,the elongation of the wire increases from $1 \ mm$ to $1.8 \ mm$. The work done during the elongation of the wire is (Acceleration due to gravity $= 10 \ m/s^2$)

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