Project ForgeThe 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. Assume that there is no friction anywhere and all other components are massless and rigid. 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.
Explanation
For an ideal (unloaded, frictionless, massless-link) Watt governor, force balance on a ball gives the classic result h=g/ω², independent of arm length or the sleeve linkage below (which carries no net force here since it's massless and frictionless). Since h∝1/ω², doubling ω quarters h: h_new=400/4=100 mm.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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