Question

A flywheel in a system is shifted to another shaft which rotates at double the speed of earlier one. The coefficient of fluctuation of speed compared to earlier case for the same fluctuation of energy is

• A. Same
• B. Doubled
• C. Reduce to $1/4$
• D. Reduce to $1/2$

Answer 1

The correct option is C Reduce to $1/4$

${\omega }_2=2{\omega }_1$

$C_s=\frac{{\omega }_{max}-{\omega }_{min}}{\left(\frac{{\omega }_{max}+{\omega }_{min}}{2}\right)}$

$\Delta E=I{\omega }^2{C}_s$

$I{\omega }_1^2{C}_{s1}=I{\omega }_2^2{C}_{s2}$ (For same $\Delta E$)

$C_{s2}=\frac{1}{4}{C}_{s1}$