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GATE 2021 ME (ME2) – Question 26

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

The controlling force curves P, Q and R for a spring controlled governor are shown in the figure, where $r_1$ and $r_2$ are any two radii of rotation.

Three controlling-force curves P,Q,R plotted against radius, with marked radii r1 and r2. See the attached source image.
  1. P unstable,Q stable,R isochronous
  2. P unstable,Q isochronous,R stable
  3. P stable,Q isochronous,R unstable
  4. P stable,Q unstable,R isochronous

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Show answer and explanation

Correct answer: (B) P unstable,Q isochronous,R stable

Explanation

Equilibrium speed satisfies $\omega^2=F/(mr)$. For P, the positive force-axis intercept makes F/r decrease with r, giving instability.

Q passes through the origin, so F/r and speed are constant: isochronous. R has a negative force intercept, making F/r increase with r: stable. **Answer: B**.