Question

Moment of inertia depends on

• A. Distribution of particles
• B. Mass
• C. Position of axis of rotation
• D. All of these

Answer 1

Answer: (A), (B), (C), (D)

All of these

Answer 2

The moment of inertia (I) of a body is a measure of its resistance to angular acceleration. It depends on several factors:

1. Mass: The moment of inertia is directly proportional to the mass of the body. A more massive body will have a greater moment of inertia, assuming the distribution of mass and axis of rotation are similar. For a system of particles, $I = \sum m_i r_i^2$, where $m_i$ is the mass of each particle.

2. Distribution of mass: The moment of inertia depends on how the mass is distributed relative to the axis of rotation. Particles farther away from the axis contribute more to the moment of inertia due to the $r^2$ term in the formula.

3. Position of axis of rotation: The moment of inertia is always calculated with respect to a specific axis of rotation. Changing the position or orientation of the axis of rotation will generally change the moment of inertia, even for the same body. The Parallel Axis Theorem ($I = I_{CM} + Md^2$) explicitly shows this dependence.

Since moment of inertia depends on all three factors (mass, distribution of particles, and position of the axis of rotation), the most comprehensive correct answer is "All of these".