Question

If the rotating mass of a rim type flywheel is distributed on a second rim type flywheel whose mean radius is half the mean radius of the former, then the energy stored in the second flywheel at the same speed will be ------- times that of the first flywheel

• A. \( \dfrac{1}{4} \)
• B. \( \dfrac{1}{2} \)
• C. \( 2 \)
• D. \( 4 \)

Hint:

For rim type flywheels at the same speed, energy stored is proportional to the square of radius.

Answer 1

The Correct Option is A

Step 1: Formula for energy stored in a flywheel.
The kinetic energy stored in a flywheel is given by: \[ E = \frac{1}{2} I \omega^2 \] For a rim type flywheel, moment of inertia \( I = mr^2 \).
Step 2: Comparing the two flywheels.
Let the radius of the first flywheel be \( r \). Then, radius of the second flywheel is \( \frac{r}{2} \).
Step 3: Ratio of energies.
\[ \frac{E_2}{E_1} = \frac{m\left(\frac{r}{2}\right)^2}{mr^2} = \frac{1}{4} \]
Step 4: Conclusion.
The energy stored in the second flywheel is one-fourth of that stored in the first flywheel.