One end of a uniform wire of length $\mathcal{l}$ and weight W is attached to a point in the roof and weight W/2 is suspended from the lower end. If A is the area of cross section of the wire then stress in the wire at its mid point is 

The stress at the midpoint of the wire is given by:

$\mathrm{Stress}=\frac{\mathrm{F}}{\mathrm{A}}$

So, the stress at the midpoint of the wire is equal to the weight of half the wire (W/2) divided by the cross-sectional area of the wire (A).

$\mathrm{F}=\frac{\mathrm{W}}{2}+\frac{\mathrm{W}}{2}$

$\mathrm{F}=\mathrm{W}$

Thus,

$\mathrm{Stress}=\frac{\mathrm{W}}{\mathrm{A}}$

Hence the correct answer is $\frac{\mathrm{W}}{\mathrm{A}}.$