Two wires of the same diameter and the same material have lengths $l$ and $2l$. If the same force $F$ is applied to each,what is the ratio of the work done in stretching the two wires?

The elastic potential energy of a strained body is

If the work done in stretching a wire by $1 \ mm$ is $2 \ J$,the work necessary for stretching another wire of the same material but with double the radius of cross-section and half the length by $1 \ mm$ is:

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

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

$A$ metal wire of length $L$ is suspended vertically from a rigid support. When a body of mass $M$ is attached to the lower end of the wire,the elongation in the wire is $l$. Consider the following statements:
$(I)$ The loss of gravitational potential energy of mass $M$ is $Mgl$.
$(II)$ The elastic potential energy stored in the wire is $Mgl$.
$(III)$ The elastic potential energy stored in the wire is $\frac{1}{2} Mgl$.
$(IV)$ The heat produced is $\frac{1}{2} Mgl$.
Which of the following statements are correct?