Question $3(30$ points$)$

A cylindrical container with diameter $D$ has a liquid with specific weigth $.$ The distance from the

bottom of the container to the surface of the liquid is $H.$

A cylindrical rod with diameter $\frac{D}{2},$ heigth $h,$ has weigth $W,$ is placed inside the container. At

equilibrium, the surface of the liquid reaches exactly the middle of the heigth of the rod.

Derive an equation to determine the change in heigth of the surface of the liquid $Y.$