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ESE Mechanical 2013 Official Paper - 2

Option 2 : is an unstable governor

Stability of Governor:

- For a **stable governor,** if the equilibrium speed increases, the radius of governor balls must also increase.

- A governor is said to be **unstable** if the radius of rotation decreases as the speed increases.

- A governor is said to be **isochronous**, when the equilibrium speed is constant (i.e., range of speed is zero) for all radii of rotation of the balls within the working range, neglecting friction.

For stable governor:

\(\frac{dF}{dr}>\frac{F}{r}\)

**Calculation:**

\(\frac{dF}{dr}=\frac{38-14}{6-2}=6\;N/cm\)

\(\frac{F_1}{r_1}=\frac{14}{2}=7\;N/cm\)

\(\frac{F_2}{r_2}=\frac{38}{6}=6.33\;N/cm\)

Here \(\frac{dF}{dr}<\frac{F_1}{r_1}\;or \;\frac{F_2}{r_2}\)

So the governor is unstable.