Question

A governor is said to be stable, if the radius of rotation of balls

• A. increases as the equilibrium speed decreases
• B. decreases as the equilibrium speed decreases
• C. increases as the equilibrium speed increases
• D. decreases as the equilibrium speed increases

Hint:

For a centrifugal governor to operate stably: - High Speed $\rightarrow$ Large Radius $\rightarrow$ Lifts Sleeve $\rightarrow$ Throttles Fuel Down. - Low Speed $\rightarrow$ Small Radius $\rightarrow$ Lowers Sleeve $\rightarrow$ Opens Fuel Up. If the radius decreased as speed increased, it would open the fuel valve further, causing the engine to accelerate uncontrollably!

Answer 1

The Correct Option is C

Concept: A centrifugal governor regulates the mean speed of an engine by adjusting the fuel supply when load fluctuations cause changes in speed. For a governor to be considered stable, it must satisfy a clear equilibrium condition:
• There must be a single, unique equilibrium speed for every specific radius of rotation of the governor balls across its entire operating range.
• If the engine speed increases due to a reduction in load, the governor balls must move outward due to the increased centrifugal force, thereby increasing the radius of rotation. This outward movement lifts the control sleeve mechanism, which throttles down the fuel supply valve to bring the engine speed back down to its target value. Mathematically, this stability condition means that the derivative of the equilibrium speed $\omega$ with respect to the radius of rotation $r$ must be strictly positive: \[ \frac{d\omega}{dr} > 0 \] This derivative confirms that a stable governor configuration requires the equilibrium speed to increase as the radius of rotation increases. This matches Option (C).