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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. 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.

1. 50
2. 100
3. 150
4. 200

Correct answer: 100

Solution

For a Watt governor, h = g/omega^2, so h is inversely proportional to omega squared. Doubling omega divides h by 4, giving 400/4 = 100 mm.

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