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?

If the tension on a wire is removed at once,then

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

The elastic energy stored in a wire of Young's modulus $Y$ is

$A$ 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?

If $x$ longitudinal strain is produced in a wire of Young's modulus $y,$ then energy stored in the material of the wire per unit volume is