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GATE 2022 ME (ME1) – Question 17

Theory of Machines · Flywheels and governors · 1 mark · Multiple choice

The figure shows a schematic of a simple Watt governor mechanism with the spindle O$_1$O$_2$ rotating at an angular velocity $\omega$ 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 O$_1$ is denoted by $h$. The value of $h = 400$ mm at a certain $\omega$. If $\omega$ is doubled, the value of $h$ will be _________ mm.

a Watt governor with the upper arms $l_1$ from the pivot O₁ to the balls P and S, and the lower links $l_2$ and $l_3$ down to the sleeve QR on the spindle.
  1. 50
  2. 100
  3. 150
  4. 200

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Correct answer: (B) 100

Explanation

For a Watt governor (the arms meeting at the pivot on the axis, with the lower arms attached to the balls), the height satisfies $h = \frac{g}{\omega^2}$. Doubling $\omega$ makes $h$ one fourth: $\frac{400}{4} = 100$ mm.