$A$ 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

$A$ uniform rod of length $L$ has a mass per unit length $\lambda$ and area of cross-section $A$. If the Young's modulus of the rod is $Y$,then the elongation in the rod due to its own weight is:

If $S$ is stress and $Y$ is Young's modulus of the material of a wire,the energy stored in the wire per unit volume is

$A$ wire $2 \,m$ in length suspended vertically stretches by $10 \,mm$ when a mass of $10 \,kg$ is attached to the lower end. The elastic potential energy gained by the wire is ...... $J$ (take $g=10 \,m/s^2$)

$A$ steel uniform rod of length $2L$,cross-sectional area $A$,and mass $M$ is set rotating in a horizontal plane about an axis passing through its center with angular velocity $\omega$. If $Y$ is the Young's modulus for steel,find the total extension in the length of the rod.

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1: 4$,the ratio of their diameters is