Correct Answer - Option 4 : 0.05

__Concepts:__

**Fluctuation of speed: **

- The difference between the
** maximum** and **minimum** speeds** during the cycle** is called **maximum fluctuation of speed.**
- The
** ratio of maximum **fluctuation of speed to the **mean speed** is known as the **coefficient of fluctuation of speed. **

**Coefficients of fluctuations** of speed when **N (rpm)** is given:

\({C_s} = \frac{{{N_1}\;-\;{N_2}}}{{{N_{mean}}}}\)

**Coefficients of fluctuations** of speed when **angular velocity (ω)** is given:

\({C_s} = \frac{{{\omega _1}\;-\;{\omega _2}}}{{{\omega _{mean}}}}\)

**We know that,**

**\({N_{mean}} = \frac{{{N_1}\;+\;{N_2}}}{2},\;and\)**

**\({\omega _{mean}} = \frac{{{\omega _1}\;+\;{\omega _2}}}{2}\)**

__Calculation:__

__Given:__

N_{1 }= 410 rpm_{, }N_{2 }= 390 rpm.

\({C_s} = \frac{{{N_1}\; - \;{N_2}}}{{\frac{{{N_1}\; +\; {N_2}}}{2}}}\)

\(C_s= \frac{{410\; - \;390}}{{\frac{{410 \;+ \;390}}{2}}}= \frac{{20}}{{400}} = \;\;0.05\)

**Coefficient of steadiness: **

The** reciprocal** of the coefficient of** fluctuation of speed** is known as the **coefficient of steadiness**. It is denoted by **(m)**.

\(m = \frac{1}{{{C_s}}}\; = \;\frac{{{N_{mean}}}}{{{N_1} - {N_2}}}\)