$A$ 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 ....... $J$

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

The work done in increasing the length of a $1 \ m$ long wire of cross-section area $1 \ mm^2$ by $1 \ mm$ will be ....... $J$ $(Y = 2 \times 10^{11} \ Nm^{-2})$

The work done in stretching an elastic wire per unit volume is

Two wires of the same material (Young's modulus $Y$) and same length $L$ but radii $R$ and $2R$ respectively are joined end to end and a weight $W$ is suspended from the combination as shown in the figure. The elastic potential energy in the system is

$A$ wire of length $25 \ cm$ and radius $2 \ mm$ is fixed at one end. If a torque is applied at the other end to produce an angular displacement of $45^o$,calculate the work done in $J$. (Given: $\eta = 8 \times 10^{10} \ N/m^2$)