6. (15 points) From a homogeneous straight rod, a piece of length $s=80 \mathrm{~cm}$ was cut. By how much did the center of gravity of the rod move as a result?
Answer: $40 \mathrm{~cm}$

Solution. The center of gravity of the original rod was located at a distance of $\frac{l}{2}$ from its end, where $l$ is the length of the rod. After cutting off a piece of the rod, its center will be at a distance of $\frac{l-s}{2}$ from the other end. Therefore, the center of gravity of the rod has moved by $\frac{s}{2}=40 \mathrm{~cm}$