A bar with circular cross-sections is supported at the top end and is subjected to a load of $P$ as shown in Figure below. The length of the bar is $L$. The weight density of the materials is $ρ$ per unit volume. It is required that the stress at every point is constant $σa$. Determine the equation for the cross-section of the bar.
I used $\pi y^2$ formula for a rotation around the $x$ axis, using $\operatorname{density} \cdot \operatorname{volume}$ to obtain mass then multiplying by $g$ ($9.81$) then adding the force $P$. Using the addition of the $2$ forces and dividing them by $\pi y^2$ I calculated the stress.
Not sure if I have done it right or if there is anything more that needs to be calculated.