# The speed of an engine varies from 110 rad/s to 90 rad/s. During cycle, the change in kinetic energy is found to be 200 N-m. The inertia of the flywhe

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The speed of an engine varies from 110 rad/s to 90 rad/s. During cycle, the change in kinetic energy is found to be 200 N-m. The inertia of the flywheel in kg-m2 is:

1. 0.2
2. 0.8
3. 0.1
4. 0.4

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Correct Answer - Option 3 : 0.1

Concept:

As the speed of the flywheel changes from maximum and minimum speeds i.e. ω1 to ω2, the maximum fluctuation of energy:

${\rm{Δ }}E = I{ω ^2}{C_s}$

Mean Speed, $ω = \frac{{{ω _1}\ +\ {ω _2}}}{2}$

Coefficient of fluctuation of speed, ${C_s} = \frac{{{ω _1}\ -\ {ω _2}}}{ω }$

Calculation:

Given:

ω1 = 110 rad/s, ω2 = 90 rad/s, ΔE = 200 N-m

$ω = \frac{{{ω _1}\ +\ {ω _2}}}{2} =\frac{110\;+\;90}{2}=100$ rad/s

${C_s} = \frac{{{ω _1}\; - \;{ω _2}}}{ω } = \frac{{110\ -\ 90}}{{100}} = \frac{{20}}{{100}}=0.2$

$I= \frac{{{\rm{Δ }}E}}{{{ω ^2}{C_s}}} = \frac{{200}}{{{{\left( {100} \right)}^2}\ \times\ 0.2}} = 0.1$