Question
Question: A smooth cylindrical gate is pivoted at its axis, with one side liquid and on other side atmosphere,...
A smooth cylindrical gate is pivoted at its axis, with one side liquid and on other side atmosphere, then
The question is incomplete and requires options to be answered.
Solution
The problem describes a cylindrical gate pivoted at its axis, with liquid on one side and atmosphere on the other. The liquid exerts a hydrostatic pressure, creating a force and a moment on the gate that tends to rotate it outwards. The atmosphere exerts pressure on the other side, creating a force and a moment that tends to rotate it inwards. The net moment about the pivot determines whether the gate rotates and in which direction. Without specific options, a definitive answer cannot be provided. The magnitude of these moments depends on the density of the liquid, the atmospheric pressure, the radius of the gate, and the extent to which the gate is filled with liquid.