The figure shows a schematic of a simple Watt governor mechanism with the spindle O₁O₂ rotating at an angular velocity ω about a vertical axis. The balls at P and S have equal mass. The vertical distance between the horizontal plane of rotation of the balls and the pivot O₁ is denoted by h. The value of h = 400 mm at a certain ω. If ω is doubled, the value of h will be _________ mm.