The moment of interia of a body depends upon

Options

A. The mass of the body
B. The distribution of the mass in the body
C. The axis of rotation of the body
D. All of these

Answer

To determine the factors on which the moment of inertia of a body depends, we can break down the analysis into several key steps:

### Step 1: Understanding Moment of Inertia
The moment of inertia (I) is a measure of an object's resistance to changes in its rotational motion. It is analogous to mass in linear motion.

### Step 2: Formula for Moment of Inertia
The moment of inertia is calculated using the formula:
\[ I = \sum m_i r_i^2 \]
where \( m_i \) is the mass of each particle and \( r_i \) is the distance of each particle from the axis of rotation.

### Step 3: Dependence on Mass
From the formula, we can see that the moment of inertia depends directly on the mass of the body. The greater the mass, the greater the moment of inertia.

### Step 4: Dependence on Distance from Axis of Rotation
The moment of inertia also depends on the distance of the mass from the axis of rotation. If the mass is further away from the axis, the moment of inertia increases because \( r^2 \) increases.

### Step 5: Dependence on Axis of Rotation
The moment of inertia is also dependent on the axis about which it is calculated. Different axes will yield different moments of inertia for the same body due to the varying distribution of mass relative to the axis.

### Step 6: Dependence on Mass Distribution
For continuous mass distributions, the way mass is distributed around the axis of rotation significantly affects the moment of inertia. A body with mass concentrated further from the axis will have a higher moment of inertia compared to one with mass concentrated closer to the axis.

### Conclusion
In summary, the moment of inertia of a body depends on:
1. The mass of the body.
2. The axis of rotation.
3. The distribution of mass relative to the axis of rotation.

Thus, the correct answer is that the moment of inertia depends on the mass, the axis of rotation, and the distribution of mass.

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