A uniform wire of length $L$ and radius $r$ is twisted by an angle $\alpha$. If modulus of rigidity of the wire is $\eta$, then the elastic potential energy stored in wire, is ………

When a block of mass $M$ is suspended by a long wire of length $L$, the length of the wire become $(L+l) .$ The elastic potential energy stoped in the extended wire is :

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

An Indian rubber cord $L$ metre long and area of cross-section $A$ $metr{e^2}$ is suspended vertically. Density of rubber is $D$ $kg/metr{e^3}$ and Young's modulus of rubber is $E$ $newton/metr{e^2}$. If the wire extends by $l$ metre under its own weight, then extension $l$ is

An aluminium rod with Young's modulus $Y =7.0$ $\times 10^{10} N / m ^2$ undergoes elastic strain of $0.04 \%$. The energy per unit volume stored in the rod in SI unit is: