Sensitiveness of governor is given by

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  1. \(\dfrac{N_1+N_2}{N}\)
  2. \(\dfrac{N_1-N_2}{N}\)
  3. \(\dfrac{N}{N_1 - N_2}\)
  4. \(\dfrac{N}{N_1 + N_2}\)

Answer (Detailed Solution Below)

Option 2 : \(\dfrac{N_1-N_2}{N}\)
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Detailed Solution

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Explanation:

Consider two governors A and B running at the same speed

  • When this speed increases or decreases by a certain amount, the lift of the sleeve of governor A is greater than the lift of the sleeve of governor B.
  • It is then said that governor A is more sensitive than the governor B

In general, the greater the lift of the sleeve corresponding to a given fractional change in speed, the greater is the sensitiveness of the governor

Sensitiveness is defined as the ratio of the difference between the maximum and minimum equilibrium speeds to the mean equilibrium speed.

\({\rm{Sensitiveness = }}\frac{{{\rm{Range}}\,{\rm{of}}\,{\rm{Speed}}}}{{{\rm{Mean}}\,{\rm{Speed}}}} = \frac{{{\omega _{\max }}\;-\;{\omega _{\min }}}}{{{\omega _{{\mathop{\rm m}\nolimits} ean}}}}=\frac{N_{max}-N_{min}}{N_{mean}}\)

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

 

Sensitivity:

It is the reciprocal of sensitiveness.

Sensitivity = \(\dfrac{N}{N_1 - N_2}\)

Thus when a governor behaves as isochronous i.e. range of speed is zero, then it is the stage of infinite sensitivity.

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