1. Find the minimum value of h for which the gate shown will rotate counterclockwise if the gate cross section is (a) rectangular, 4 ft × 4 ft; (b) triangular, 4 ft at the base × 4 ft high. Neglect bearing friction.
2. A circular log of radius r is to be used as a barrier as shown in the figure below. If the point of contact is at O, determine the required density of the log.