Question

In a centrifugal governor, the controlling force is observed to be 14 N, when the radius of rotation is 2 cm and 38 N, when the radius of rotation is 6 cm. The governor
1. is a stable governor
2. is an unstable governor
3. is an isochronous governor
4. cannot be said of what type with the given data

Answer 1

Correct Answer - Option 2 : is an unstable governor

Concept:

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.