Option 2 : 1% change in speed

__Explanation:__

**Governor Effort **

- It is the force exerted by the governor at the sleeve as the sleeve tends to move.
**When the speed of the governor is constant, the force exerted on the sleeve is zero as the sleeve doesn't tend to move and hence at the constant speed, the effort of the governor is zero,**but when the speed changes and the sleeve tends to move to new equilibrium position force is exerted on the sleeve.**This force gradually diminishes to zero as the sleeves move to a new equilibrium position corresponding to the new speed**.- The mean force exerted on the sleeve during the given change of speed is known as the effort of the governor.
**The given change of speed is generally taken as 1%, hence effort is defined as the force exerted on the sleeve for 1% change of speed.**

Option 1 : 1 percent

__Explanation:__

Governor Effort – It is the force exerted by the governor at the sleeve as the sleeve tends to move.

When the speed of the governor is constant, the force exerted on the sleeve is zero as the sleeve doesn't tend to move and hence at the constant speed, the effort of the governor is zero, but when the speed changes and the sleeve tends to move to new equilibrium position force is exerted on the sleeve.

This force gradually diminishes to zero as the sleeves move to a new equilibrium position corresponding to the new speed.

The mean force exerted on the sleeve during the given change of speed is known as the effort of the governor.

The given change of speed is generally taken as 1%, hence effort is defined as the force exerted on the sleeve for 1% change of speed.

Option 2 : 1% change in speed

__Explanation:__

**Governor Effort **

- It is the force exerted by the governor at the sleeve as the sleeve tends to move.
**When the speed of the governor is constant, the force exerted on the sleeve is zero as the sleeve doesn't tend to move and hence at the constant speed, the effort of the governor is zero,**but when the speed changes and the sleeve tends to move to new equilibrium position force is exerted on the sleeve.**This force gradually diminishes to zero as the sleeves move to a new equilibrium position corresponding to the new speed**.- The mean force exerted on the sleeve during the given change of speed is known as the effort of the governor.
**The given change of speed is generally taken as 1%, hence effort is defined as the force exerted on the sleeve for 1% change of speed.**

Option 3 : zero

__ Explanation__:

**Isochronism**:

- A governor with a
**range of speed zero**is known as an**isochronous governor**. - During this situation,
**for all positions**of the sleeve or the balls, the governor has the**same equilibrium speed**.

**Effort of a governor**:

The **effort** of a governor is the **mean force acting** on the sleeve to raise or lower it for a given change of speed.

∴ at **constant speed **i.e. for an **isochronous governor**, the **resulting force** acting on the governor is** zero**.

Option 3 : force acting on sleeve for given percentage change of speed

__Explanation:__

Governor Effort

- It is the force exerted by the governor at the sleeve as the sleeve tends to move.
- When the speed of the governor is constant, the force exerted on the sleeve is zero as the sleeve doesn't tend to move and hence at the constant speed, the effort of the governor is zero, but when the speed changes and the sleeve tends to move to new equilibrium position force is exerted on the sleeve.
- This force gradually diminishes to zero as the sleeves move to a new equilibrium position corresponding to the new speed.

Option 3 : zero

**Explanation****:**

**Isochronism:**

- A governor with a
**range of speed zero**is known as an**isochronous governor**. - During this situation,
**for all positions**of the sleeve or the balls, the governor has the**same equilibrium speed**.

**Effort of a governor:**

The **effort** of a governor is the **mean force acting** on the sleeve to raise or lower it for a given change of speed.

∴ at **constant speed **i.e. for an **isochronous governor**, the **resulting force** acting on the governor is** zero**.

Option :

__Concept:__

A simple pinned watt governor is shown below with forces acting on it.

F_{c} = mrω^{2}; W = mg;

Let θ be the angle made by arm with the axis of sleeve and L be the length of the upper arm.

\(\tan \theta = \frac{{{F_c}}}{W} = \frac{{mr{\omega ^2}}}{{mg}} = \frac{{r{\omega ^2}}}{g}\) -----(1)

\(\cos \theta = \frac{h}{L}\) -----(2)

\(\sin \theta = \frac{r}{L}\) -----(3)

Combining 1 and 3 and eliminating r,

\({\omega ^2} = \frac{g}{{L\cos \theta \;}} = \frac{g}{h}\) ----(4)

If c be the speed factor,

\(c = \frac{{{\omega _2} - {\omega _1}}}{{{\omega _1}}}\)

Effort of the governor will be E = cmg

__Calculation:__

Given θ_{1} = 30°, θ_{2} = 45°, m = 2 kg, L = 30 cm = 0.3 m;

**Case 1:**

**θ _{1} = 30°, L = 0.3 m, **

h_{1} = L cos θ_{1} = 0.3 × cos 30° = **259.8 mm** (**Option 1 is wrong**)

\(\omega _1^2 = \frac{g}{{{h_1}}} = \frac{{9.81}}{{0.2598}} = 37.76\)

⇒ **ω _{1} = 6.14 rad/s**

**Case 2:**

**θ _{2} = 45°, L = 0.3 m, **

h_{2} = L cos θ_{2} = 0.3 × cos 45° = **212.1 mm** (**Option 2 is wrong**)

\(\omega _2^2 = \frac{g}{{{h_2}}} = \frac{{9.81}}{{0.2121}} = 46.24\)

⇒ **ω _{2} = 6.8 rad/s**

Speed factor c is

\(c = \frac{{6.8 - 6.14}}{{6.8}} = 0.097\) (**Option 3**)

Effort of the governor = cmg = 0.097 × 2 × 9.81 = **1.9 N** (**Option 4**)

Option 1 : 1 percent

__Explanation:__

Governor Effort – It is the force exerted by the governor at the sleeve as the sleeve tends to move.

When the speed of the governor is constant, the force exerted on the sleeve is zero as the sleeve doesn't tend to move and hence at the constant speed, the effort of the governor is zero, but when the speed changes and the sleeve tends to move to new equilibrium position force is exerted on the sleeve.

This force gradually diminishes to zero as the sleeves move to a new equilibrium position corresponding to the new speed.

Option 2 : 1% change in speed

__Explanation:__

**Governor Effort **

- It is the force exerted by the governor at the sleeve as the sleeve tends to move.
**When the speed of the governor is constant, the force exerted on the sleeve is zero as the sleeve doesn't tend to move and hence at the constant speed, the effort of the governor is zero,**but when the speed changes and the sleeve tends to move to new equilibrium position force is exerted on the sleeve.**This force gradually diminishes to zero as the sleeves move to a new equilibrium position corresponding to the new speed**.