Solution

Statement

$2.3.15.$ What minimum work must be done to raise a long uniform pole of length $l$ and mass $m$ lying on the ground to a vertical position?

Solution

For a uniform pole, its center of mass is located exactly in the middle. When lying on the ground, the height of its center of mass is $0$. When placed vertically, the center of mass is raised to a height of $h = \frac{l}{2}$.

The minimum work done is equal to the increase in the potential energy of the center of mass:
$$A = mgh = mg\frac{l}{2}$$