Question

For a certain engine having an average speed of 1200 rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within 2% of the average speed. The fluctuation of kinetic energy per cycle is found to be 2 kJ. What is the least possible mass of the flywheel if its diameter is not to exceed 1 m?

• A. 40 kg
• B. 51 kg
• C. 62 kg
• D. 73 kg

Answer 1

The correct option is B 51 kg

Average speed,
$\omega =\frac{2\pi \times 1200}{60}=125.66\text{rad/s}$

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

and $\Delta E=\frac{M{R}^2}{2}\times {\omega }^2\times C_s$

$\therefore M=\frac{2\Delta E}{R^2\times {\omega }^2\times C_s}=\frac{2\times 2000}{{\left(\frac{1}{2}\right)}^2\times (125.66{)}^2\times 0.02}$

$=50.66\approx 51kg$

Point to Remember
It is important to note that here the value of $C_s=0.02$, not $C_s=0.04$, because it is given that the fluctuation of speed within 2% about the average speed.