Question

A circular disc A and a ring B have same mass and same radius. If they are rotated with the same angular speed about their own axis, then

• A. A has less moment of inertia than B
• B. A has less rotational kinetic energy than B
• C. A and B have the same angular momentum
• D. A has greater angular momentum than B
• E. A has the same moment of inertia as that of B

Hint:

For same mass and radius, ring always has greater moment of inertia than disc.

Answer 1

The Correct Option is A

Concept: Moment of inertia: \[ I_{disc} = \frac{1}{2}mR^2, \quad I_{ring} = mR^2 \]

Step 1: Compare moment of inertia. \[ I_{disc} < I_{ring} \]

Step 2: Rotational kinetic energy. \[ K = \frac{1}{2}I\omega^2 \Rightarrow K_{disc} < K_{ring} \]

Step 3: Angular momentum. \[ L = I\omega \Rightarrow L_{disc} < L_{ring} \]

Step 4: Conclusion. Options (A) and (B) are correct.